Happy New Year Premath, Please God a good one watching your fine content

@PreMath

Жыл бұрын

Happy new year! Thanks for your continued love and support! You are awesome, John. Keep it up 👍 Love and prayers from the USA! 😀 Stay blessed 😀

@ramanivenkata3161

Жыл бұрын

@@PreMath Thank you for your New year Greetings which I Heartily Reciprocate.

Think outside the box : imagine the yellow triangle to be a rectangel area 240 units . Thus , everything falls right in place beautifully . Thank you .

@PreMath

Жыл бұрын

Excellent! Thanks for sharing! Cheers! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀 Stay blessed 😀

@majorbuzz

Жыл бұрын

That's how I solved it , too.

@Destroyer-db5vn

Жыл бұрын

That is how I solved it

@thephilosophyofhorror

Жыл бұрын

Indeed :) But I had to be hipster and instead turn the parallelogram to a triangle. Your idea is a lot better.

@TampaCEO

Жыл бұрын

That's literally how I solved the problem. Start by turning the 120 area triangle into a 240 area rectangle and the problem is solved.

1. Convert the 120 area triangle into a 240 area rectangle. 2. Calculate the combined area of the BOTH rectangles. 768 + 240 = 1008. 3. Divide 1008 by the top line (42) to give us the length of the right line as 24. 4. Divide the area of the left rectangle (240) by 24 to get 10 (the base of the left triangle) 5. Subtract the base of the left triangle from 42 to get 32 (the bottom line) 6. Calculate the length of the hypotenuse as 24 squared plus 10 squared to get 676. The square root comes to 26. Answer: 24, 32, 26.

@PreMath

Жыл бұрын

Excellent! Thanks for sharing! Cheers! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀 Stay blessed 😀

@luispnrf

Жыл бұрын

I did it this way.

42 / (2 * 120 + 768) * 240 = 10 (width of orange triangle) 240 / 10 = 24 (height of both figures) √(10² + 24²) = √(100 + 576) = √676 = 26 (hypotenuse of orange triangle) 42 - 10 = 32 (width of green rectangle)

@PreMath

Жыл бұрын

Super! Thanks for sharing! Cheers! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀 Stay blessed 😀

If you wanted to avoid the system of equations, you can also divide the parallelogram into two triangles, each with area 384, and since that new triangle shares a height with the 120 one, it follows its own base would be 384/120=3.2 times larger. So 3.2x+x=42=> x=10 =>y (the height) is 24, x2 is 42-x=32, hypotenuse (pyth theorem) is 26.

@PreMath

Жыл бұрын

Thanks for sharing! Cheers! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀 Stay blessed 😀

@txt.myhome7979

8 ай бұрын

I did it the same way

A different approach would be to complete the rectangle. Spoiler alert: 768 + 2 ∙ 120 = 1008; 1008 / 42 = 24 = h; 768 / 24 = 32 = a; 42 − 32 = 10 = x; 10² + 24² = c², but this is just a scaled 5-12-13 triangle, so c = 26.

@PreMath

Жыл бұрын

Thanks for sharing! Cheers! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀 Stay blessed 😀

I love these! Thanks!

That is very nice . Thanks premath

I am so happy. I got one right without having to cheat or fix something that I stuffed up. Yay, cartwheels and stuff!

Perfect Video thanks so much

At a quick glance: Forming a rectangle by doubling the triangular area. The height of the trapezoid is (768+ 120*2)/ 42 =24. The base pf the trapezoid is 768/24 = 32. Base of the triangle is 42 - 32 = 10 and unknown side length = sqrt( 100 + 576) = 26. The unknown lengths of the trapezoid = 26 , 32 and 24.

I did it using trapezoid formula as the total area is known (888) as is the longest side 42. Then as side and small base are both height and base of trapezoid and side and base of rectangle I just substituted them. Their product also known 768. In my case I ended up with 21h = 888-768/2 = 504 h=504/21=24

@PreMath

Жыл бұрын

Thanks for sharing! Cheers! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀 Stay blessed 😀

I watch your videos daily without delay you are very good teacher thankyou to help us

@PreMath

Жыл бұрын

So nice of you, Jay Thank you! Cheers! Glad to hear that! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀 Stay blessed 😀

I went a slightly different route but got there in the end. Your way was better :)

From formula for area of triangle xy = 240 From formula for area of rectangle (42-x)y=768 42y -xy = 768 42y - 240 = 768 42y = 768+240 42y = 1008 y = 24 x = 10 From Pythagorean identity z^2=24^2+10^2 z^2=676 z=26 Missing side lengths (24,32,26) Quite easy

Nice bicolor task on planimetry. I remember area of triangle and trapeze were my favourite things in my scholar years. Thank you so much for this souvenir of my childhood:)) You are really the best teacher and the man as well

@PreMath

Жыл бұрын

You are so welcome! So nice of you, Anatoliy Thanks for your continued love and support! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀 Stay blessed and safe 😀

Thank you for video. This one is really simple and easy.

@PreMath

Жыл бұрын

You bet! Thank you! Cheers! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀 Stay blessed 😀

Very well explained👍 Thanks for sharing😊

@PreMath

Жыл бұрын

My pleasure 😊 You are awesome. Keep it up 👍 Love and prayers from the USA! 😀 Stay blessed 😀

I loved it

Thanks Sir

So satisfying!

@PreMath

Жыл бұрын

Glad you think so! Thanks for your feedback! Cheers! You are awesome, Ludwig. Keep it up 👍 Love and prayers from the USA! 😀 Stay blessed 😀

Nice! (42 - b)a = 768 ab/2 = 120 → a = 240/b → (42 - b)a = (42 - b)(240/b) = 768 → 240(42)/b = 1008 → b = 240(42)/24(42) = 10 → 42 - b = 32 → a = 24 → tan⁡(φ) = sin⁡(φ)/cos⁡(φ) = 5/12 → sin⁡(φ) = (5/12)cos⁡(φ) sin^2(φ) + cos^2(φ) = 1 → sin⁡(φ) = √(1 - cos^2(φ)) → (5/12)cos⁡(φ) = √(1 - cos^2(φ)) → 1 - cos^2(φ) = (25/144)cos^2(φ) → 1 = (169/144)cos^2(φ) → cos⁡(φ) = (12/13) = (24/k) → k = 13(24/12) = 26 = c 🙂 fast lane: 10-24 → c = 26 (Pyth. Triple 2(5-12-13)) 🙂

@PreMath

Жыл бұрын

Excellent! Thanks for sharing! Cheers! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀 Stay blessed 😀

Gr8 sir

@PreMath

Жыл бұрын

Glad you think so! Thanks for your feedback! Cheers! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀 Stay blessed 😀

Thanks for video.Good luck sir!!!!!!!!!!!!

@PreMath

Жыл бұрын

Thank you too You are awesome. Keep it up 👍 Love and prayers from the USA! 😀 Stay blessed 😀

Quadrangle sides named clockwise: 42; H; B; A → H=(768+120+120)/42=24 → B=768/24=32 → A²=(42-32)²+24²=676→A=√676=26

@PreMath

Жыл бұрын

Excellent! Thanks for sharing! Cheers! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀 Stay blessed 😀

Nice example, I just added another triangle to the end to make a rectangle Which added 120 area more, then just did the arithmetic

Answers 24, 26, and 32 let the base of the triangle = b, and let the height = n, then (b)(n) =240 but n is also the width of the rectangle and 42-b the length; hence the area of the rectangle is : (42-b)(n) = 768 42n-bn =768 42n- 240= 768 since bn=240 42n=1,008 n = 24; hence b =10 So, the width of rectangle=n= the height of triangle =24 answer The base of the triangle, b= 10 The length of the rectangle is 42-10= 32 answer The hypotenuse of the triangle is the square root of 24^2 + 10^2 = sqrt 676 =24

@PreMath

Жыл бұрын

Excellent! Thanks for sharing! Cheers! You are awesome, Devon. Keep it up 👍 Love and prayers from the USA! 😀 Stay blessed 😀

Yay, I solved it. My method was the same as the video solution.

@PreMath

Жыл бұрын

Excellent! Glad to hear that! Thanks for sharing! Cheers! You are awesome, Mark. Keep it up 👍 Love and prayers from the USA! 😀 Stay blessed 😀

Nice

Let a be the height of the trapezoid/width of the rectangual portion. Let b be the length of the shorter parallel side, and c be the additional length of the longer parallel side, so c = 42 - b. Them a b = 768 and a c = 240, so b / c = 16 / 5, so b + c = 21/16 b, so 21/16 b = 42, so b = 32, c = 10 and a = 24.

a and b length and width of the rectangle, c hypothenuse of the triangle ( a, b, and c are the sizes of the sides of the trapezoid other than 42) ab=768 (b(42-a)/2)=120 42b-768=240 42b=1008 b=24 a=32 c=sqrt((42-a)^2+b^2)=sqrt((42-32)^2+24^2)=sqrt(10^2+24^2)=sqrt(100+576)=sqrt(676)=26 Answers: 24 (vertical), 32 (smaller horizontal), 26 (oblique)

@PreMath

Жыл бұрын

Excellent! Thanks for sharing! Cheers! You are awesome, Serouj. Keep it up 👍 Love and prayers from the USA! 😀 Stay blessed 😀

You can do it other way Join diagonal of the rectangle such that you get a large triangle with base 42 and breadth as height Equate to area you will get breadth and so you will get length and the third side can be found by using Pythagoras theorem

The yellow right triangle is a Pythagorean triplet of 5, 12, & 13- this one multiplied by 2. The 5, 12, & 13 triplets is just about as common as the 3, 4, & 5 one, as I’m sure you know. I think it would be good for you to point out these triplets so your viewers can learn about them.

xy=768 (42-x)y/2=120 y=768/x y=240/(42-x) 768/x=240/(42-x) 768(42-x)=240x 32256-768x=240x 32256=1008x x=32 y=24 √[24²+(42-32)²]=√[576+100]=√676=26 (24 , 32 , 26)

@PreMath

Жыл бұрын

Excellent! Thanks for sharing! Cheers! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀 Stay blessed 😀

I'm learning thanks to Sir This one I managed to get right Grateful Congratulations 👏🇧🇷

@PreMath

Жыл бұрын

Excellent! Glad you think so! Thanks for your feedback! Cheers! You are awesome, Alex. Keep it up 👍 Love and prayers from the USA! 😀 Stay blessed 😀

@alexrocha9191

Жыл бұрын

@@PreMath Good Morning Master A Hug From Brazil 🇧🇷 Congratulations 👏👏👏

768+120+120=1008 h=1008/42=24 768+120=888 area=h(l+s)/2 l = long length and s=short length s=((888*2)/24)-42=32 42-32=10 a^2+b^2=c^2 10^2+24^2=c^2=676 c=26 h=24, s=32, c=26

@PreMath

Жыл бұрын

Excellent! Thanks for sharing! Cheers! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀 Stay blessed 😀

I solved it by myself without any pen or paper ..... Ohh....😁😁fun ...it was

@PreMath

Жыл бұрын

Super! Thanks for sharing! Cheers! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀 Stay blessed 😀

Thanks 🙏🙏🙏

@PreMath

Жыл бұрын

You are very welcome! So nice of you, Yuusuf Thank you! Cheers! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀 Stay blessed 😀

Assume bottom = Y , height =X X*Y=768 X*(42-Y)/2=120 so X =24 Y=32

As a triangle, the yellow area is equal to its base times height, all divided by two. As a rectangle, the green area is equal to its width times its height. Thus the triangle has half the area of a rectangle of the same dimensions. So since we know the combined width of both areas and that they share the same height, if we assume the triangle is a rectangle and double its area, we can determine their individual widths from the ratios of their areas. Let b be the base (width) of the yellow section, h be the length of the right side of the trapezoid, w be the length of the bottom side/entire green area, and x be the length of the diagonal left side. b/42 = 240/(240+768) = 240/1008 b = 42(5/21) = 10 w = 42 - b = 42 - 10 = 32 units Aᵣ = wh 768 = 32h h = 768/32 = 24 units a² + b² = c² 10² + 24² = x² x² = 100 + 576 = 676 x = √676 = 26 units

I solve addimg other triangle with area equals to 120, turning the figure into a rectangle.

@PreMath

Жыл бұрын

Excellent! Thanks for sharing! Cheers! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀 Stay blessed 😀

Let measure of unknown side b =x.and perp.distance between parallel sides=h.now 240/(42-x)=768/x gives x=672/21=96/3= 32.unit is the measure of reqd.side of trapizium.ans

Very easy Math Problem

@PreMath

Жыл бұрын

Excellent! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀 Stay blessed 😀

The triangle is Pythagorean. It's 5 - 12 - 13 with sides doubled to 10 - 24 - 26.

CD=b=42 AB=a=? BC=AE=h=? DE=x=? DA=c=? Yellow triqngle - A1= x.h/2=120 x.h=240 green area A2=(42-x).h= 42.h- x.h= 42.h-240= 768, 42.h= 768+240= 1008, h=1008/42=24 x.h=240 x=240/h=10 a=42-x=42-10= 32 Yellow triangle c^2= x^2 +h^2 =10^2+24^2=100+576=676 c=26

@PreMath

Жыл бұрын

Thanks for sharing! Cheers! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀 Stay blessed 😀

@liliyakaloyanova377

Жыл бұрын

@@PreMath Thanks from Bulgaria.My best wishes , too!

@PreMath

Жыл бұрын

@@liliyakaloyanova377 Thanks dear! You are the best!

xh=768, xh÷2=768÷2=384 ((42+x)h)÷2=(768+120) 21h+xh÷2=888 21h=888-384=504 h=24 xh=768 x=32

@PreMath

Жыл бұрын

Excellent! Thanks for sharing! Cheers! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀 Stay blessed 😀

10/24/32 by hit and trial without pen and paper

@PreMath

Жыл бұрын

Thanks for sharing! Cheers! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀 Stay blessed 😀

Length=32 . Width=24. Epotenus=26

@PreMath

Жыл бұрын

Thanks for sharing! Cheers! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀 Stay blessed 😀

24, 32 ,26

24; 32; 26

24 32 26

@PreMath

Жыл бұрын

Excellent! Thanks for sharing! Cheers! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀 Stay blessed 😀

We'll explained

@PreMath

Жыл бұрын

Glad you think so! Thanks for your continued love and support! You are awesome, Ramani. Keep it up 👍 Love and prayers from the USA! 😀 Stay blessed , and a happy new year! 😀

@ramanivenkata3161

Жыл бұрын

@@PreMath Thank you very much for your New year Greetings which I Heartily Reciprocate

@PreMath

Жыл бұрын

@@ramanivenkata3161 Thanks dear! You are the best!

Ha! Solved it without watching!

补齐三角形

Sir I wanna communicate with you

@PreMath

Жыл бұрын

Please send email to premathchannel@gmail.com Thank you! Cheers! Love and prayers from the USA! 😀 Stay blessed 😀

@awwab1094

Жыл бұрын

@@PreMath thank you

а= 32; h= 24; x= 10

@PreMath

Жыл бұрын

Thanks for sharing! Cheers! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀 Stay blessed 😀

@alexniklas8777

Жыл бұрын

@@PreMath 👍❤️

768+120+120=1008

H= 24,,,,,Base = 32 and Slant length = 26...

Not very hard. Used system of linear equations to solve it

@PreMath

Жыл бұрын

Thanks for your feedback! Cheers! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀 Stay blessed 😀

24 32 26