Thank God I have a natural neural network as opposed to Artificial Intelligence. At the least I can feel real emotions when following Premath . 🙂

@PreMath

10 ай бұрын

Thanks for your feedback! Cheers! 😀 You are awesome. Keep rocking 👍

Here's a mostly algebraic solution, some tedious details omitted: Let the width of the central vertical stack of rectangles be y, and consider the lower two rectangles: 48/y = 128/10 = 12.8; so 12.8y = 48 and y = 48/12.8 = 3.75. Now for the upper two rectangles: 132/x = 36/y = 36/3.75 = 9.6; so x = 132/9.6 = 13.75. Cheers. 🤠

@PreMath

10 ай бұрын

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Height of lower rectangles: Area = 80+48=128 cm² Area = b. h h = A / b = 128 / 10 = 12,8 cm Base of green and blue rectangle: A = b. h b = A / h = 48 / 12,8 b = 3,75 cm Height of upper rectangles: A = 36 cm² = b. h h = A / b h = 36 / 3,75 h = 9.6 cm Base of yellow rectangle: A = b. h b = A / h = 96 / 9,6 b = 10 cm Length 'x' X = b₁ + b₂ = 10 + 3,75 X = 13,75 cm ( Solved √ )

@PreMath

10 ай бұрын

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@frederickdvorak6502

10 ай бұрын

That was my solution too. I had forgotten about A / B = a / b.

Another solution is to add one third to the blue and yellow rectangles (hence making the blue one = 48, same as the green). Then the upper rectangles are 176 and the lower are 128 together and X=10*176/128

Nice question.

48+80 = 128. 128/10 = 12.8. 48/12.8 = 3.75. 36/3.75 = 9.6. 96/9.6 = 10. X = 10 + 3.75 = 13.75

@PreMath

10 ай бұрын

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My route was to extend the top rectangle by 10 to the right giving three rectangles of areas 96, 36, and 60 (because it must be 3/4 of the rectangle with area 80 at the bottom). The lower rectangles have a height of 12.8 ((48+80)/10, so the upper rectangles must have a height that is 3/4 of that, so 9.6. You now have two upper rectangles whose lengths total (96+36)/9.6, which is x = 13.75. I didn't get anywhere near 55/4 but took a different path to the same place. It looks like there were multiple paths to solve this and I seem to have dug out the complicated one as usual :}

@PreMath

10 ай бұрын

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Nice explanation, but I thik is inconsistent because you've usted two different criteria in the proposed solution. First part you use área ratio between rectangles to determine the width of the green one , however, to determine "x", the method used is to calculate heigth of the Bluetooth one and then, determine the value of "x". In terms of teaching, in my opinión, we need to follow same procederé in every step to avoid confusiones. Of course, result is correct no matter the method. Congratulations.

@PreMath

10 ай бұрын

Thanks for your feedback! Cheers! 😀

Wonderful solution Thanks Sir. ❤❤❤❤❤

@PreMath

10 ай бұрын

Most welcome, dear

Good content, this make me happy when get solution

@PreMath

10 ай бұрын

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96/36=8/3， so x divided into 8:3, 80/48=5/3, so 10 divided into 3:5, hence 36 or 48 own the width 10x3/8=15/4 this the 3 in 11 of x so x=15/4x11/3=55/4.😄

@PreMath

10 ай бұрын

Excellent! Thanks for sharing! Cheers! You are awesome. Keep it up 👍

Green is 4/3 thicker than Blue, so the Green and Pink combined can be made into a new rectangle of width 10*4/3 having same height as Blue. Hence, X = (40/3)*(96+36)/(48+80) = (40/3)*(132/128)= 55/4

@PreMath

10 ай бұрын

Excellent! Thanks for sharing! Cheers! You are awesome. Keep it up 👍

(96+36)/[(36/48)(48+80)/10]=63360/4608=55/4=13.75 Gracias y un saludo.

@PreMath

10 ай бұрын

Excellent! Thanks for sharing! Cheers! You are awesome. Keep it up 👍

48 : 80 = 3a : 5a 3a+5a=10 8a=10 a=5/4 3*5/4=15/4 15/4*96/36=15/4*8/3=5*2=10 15/4+10=15/4+40/4=55/4=13.75 x = 13.75

@PreMath

10 ай бұрын

Great!

 Solution: (80+48)/10 = 12,8 = vertical side of the purple and green rectangle. 48/12,8 = 3,75 = horizontal side of the green and light blue rectangle. 36/3,75 = 9,6 = vertical side of the light blue and yellow rectangle. x = (96+36)/9,6 = 13,75[cm]

@PreMath

10 ай бұрын

Excellent! Thanks for sharing! Cheers! You are awesome. Keep it up 👍

Generalization: if green = g, purple = p, blue = b, yellow = y and the known length = k then the unknown length x = (g k (b + y)) / (b ( g + p))

@PreMath

10 ай бұрын

Excellent! Thanks for sharing! Cheers! You are awesome. Keep it up 👍

Yay! I solved it.

@PreMath

10 ай бұрын

Excellent! Thanks for sharing! Cheers! You are awesome. Keep it up 👍

(48+80)/10=12.8 36:48=3:4 12.8/4*3=9.6 (96+36)/9.6=13.75

@PreMath

10 ай бұрын

Excellent! Thanks for sharing! Cheers! You are awesome. Keep it up 👍

Nice problem ❤

@PreMath

10 ай бұрын

Glad you like it! Thanks for your feedback! Cheers! 😀 You are awesome. Keep it up 👍

48 / (48 + 80) * 10 = 36 / (36 + 96) * x 48 / 128 * 10 = 36 / 132 * x x = 48 / 128 * 10 * 132 / 36 x = 3 / 8 * 10 * 11 / 3 x = 10 * 11 / 8 x = 5 * 11 / 4 x = 55 / 4 = 13.75 cm

@PreMath

10 ай бұрын

Excellent! Thanks for sharing! Cheers! You are awesome. Keep it up 👍

x=13,75 cm

Green and purple = 128 cm2. If long side is 10, short side is 12.8. If green is 48 cm2 with one side 12.8 then other green side must be 3.75. If blue is 36 cm2 with one side 3.75 the other side must be 9.6. If yellow is 96 with one side 9.6 the other side must be 10. 10 + 3.75 = 13.75

13.75

@PreMath

10 ай бұрын

Super!

13,75

Easy

128 ÷ 10. = 12.8 48. ÷ 12.8 = 3.75. ----> (1) 36 ÷ 3.75 = 9.6 132 ÷ 9.6 = 13.75

@PreMath

10 ай бұрын

Excellent! Thanks for sharing! Cheers! You are awesome. Keep it up 👍

@mohanramachandran4550

10 ай бұрын

@@PreMath Thanks for your comments

22

If 128=10 then x=9 16/112 or x=1024/112

asnwer=13 cm or 15cm my hmm gmmm

@comdo777

10 ай бұрын

gmm hmm honst isit

I solved this question but i took 5 mins to think deeper...