great as always.

@PreMath

Ай бұрын

Glad you think so! Thanks for the feedback ❤️

Strictly speaking, the perimeter and the area cannot be equal because the unit of measurement is different for each : u vs u². But once we get over that little misnomer, the problem is actually quite pleasant.

Let's face this challenge: . .. ... .... ..... The triangle ABC is a 30°-60°-90° triangle, so we can conclude: AB = √3*BC AC = 2*BC The area and the perimeter can easily be calculated: Area = Perimeter (1/2)*AB*BC = AB + AC + BC (1/2)*(√3*BC)*BC = √3*BC + 2*BC + BC (√3/2)*BC² = BC*(√3 + 3) Since BC>0, we finally obtain: BC = (√3 + 3)*(2/√3) = 2*(1 + √3) AB = √3*BC = 2√3*(1 + √3) AC = 2*BC = 4*(1 + √3) Best regards from Germany

@PreMath

Ай бұрын

Bravo! Thanks for sharing ❤️

(30° ; 60°; 90°) So BC=x AC=x√3; AC=2x area=1/2(x)(x√3) Prerimeter=x+2x+x√3 1/2(x^2.√3)=3x+x√3 x=2√3+2 So BC=2√3+2 ; AC=4√3+4 ; AB=√3(2√3+2)=2√3+6.❤❤❤ Thanks sir.

@PreMath

Ай бұрын

Excellent! You are the best. You are very welcome! Thanks for sharing ❤️

Short side = X, long side = 2X, hypotenuse = 1.732X. Area = 0.5 *X * 1.732X. Area = 0.8660X*X. Perimeter = X + 2X + 1.732X. Perimeter = 4.732X. Then 0.8660X*X = 4.732X Divide both sides by X. 0.8660X = 4.732. X = 5.464 = short side. Long side = 5.464 * 1.732 = 9.464. Hypotenuse = 5.464 * 2 = 10.928.

@PreMath

Ай бұрын

Excellent! Thanks for sharing ❤️

Congratulationn! Basic concepts and a great question!!

@PreMath

Ай бұрын

Glad it was helpful! Thanks for the feedback ❤️

Thank you!

@PreMath

Ай бұрын

You are very welcome! Thanks ❤️

interesting for me

@PreMath

Ай бұрын

Glad to hear that! Thanks for the feedback ❤️

AB=a, BC=b, AC=2b. a^2=c^2-b^2. a^2=4b^2-b^2. a^2=3b^2, a=b\/3. P=b(\/3+3), А=b^2\/3/2. Р=А, b(\/3+3)=b^2\/3/2. b=2(\/3+1), а=2(\/3+3, с=4(\/3+1). Р=8\/3+12. А=8\/3+12.

@PreMath

Ай бұрын

Thanks for sharing ❤️

Sin 30= 1/2 So proportion of sides is 1 : 2 : 1.732 Find multiplier to satisfy a + b + c = (a + b)/2 where c=2a k=5.46 Result = 5.46, 9.46, 10.92

BC=x AB=√3x AC=2x x･√3x/2 = x+√3x+2x √3x^2/2 = 3x+√3x √3x^2 = 6x+2√3x √3x^2-6x-2√3x=0 x(√3x-6-2√3)=0 x>0 , √3x=2√3+6 x=2+2√3 BC=2+2√3 AB=6+2√3 AC=4+4√3

@PreMath

Ай бұрын

Excellent! Thanks for sharing ❤️

2(3+√3)≈9,464 2(√3+1)≈5,464 4(√3+1)≈10,93

@PreMath

Ай бұрын

Excellent! Thanks for sharing ❤️

Mmmmmm! a length cannot equal an area

Church Lady would say "well isn't that special?" 🙂

@PreMath

Ай бұрын

Your comments are always a breath of fresh air. They are very enlightening❤️

@wackojacko3962

Ай бұрын

I love you man! 🙂

that is impossible for the triangle's area equal to the triangle's perimeter, the area uses square unit but the perimeter is just the length of the triangle, it is unit.

a,2a, aqrt(3)a, sides of the triangle, and then (sqrt(3)/2)a^2=(3+sqrt*3))a=sqrt(3)(sqrt(3)+1)a, a=2(sqrt(3)+1), therefore the sides are 2(sqrt(3)+1), 4(sqrt(3)+1), 2(3+sqrt(3))😊.

@PreMath

Ай бұрын

Excellent! Thanks for sharing ❤️

Yes, I did find another way, but it's a complete headbanger compared to yours LOL. Thanks again.

Sres. Premath, reciban un cordial saludo. Gracias por el ejercicio y su procedimiento. Comentándoles: El perímetro es 12 + 8*3^0.5 unidades lineales, el área es 12 + 8*3^0.5 unidades cuadradas, cómo interpreto esto, si las unidades de medida son diferentes ??. Una inquietud más: Si el triángulo rectángulo no es un notable hay forma de dar solución al problema ??? creo que al menos se debería conocer un lado del triángulo ??? Gracias por la atención que se digne en prestarme. Éxitos.

@PreMath

Ай бұрын

Hola querido, estamos hablando de valores numéricos solo para el perímetro y el área. Gracias por los comentarios ❤️

@maxwellarregui814

Ай бұрын

@@PreMath Gracias por su atención, entendido la primera, es muy importante la segunda inquietud, agradecería su comentario. Éxitos

🥰

@PreMath

Ай бұрын

Thanks ❤️

Area and perimeter have the same numerical value.

@PreMath

Ай бұрын

Thanks for the feedback ❤️

Hello

@PreMath

Ай бұрын

Hello dear 🌹

May not agree. Give an example Hypotenuse 13 unit Base 5 unit Perpendicular 12 unit It is 13*13=169 12*12+5*5=144+25=169 Hence the lengths are of a rt triangle. Now perimeter =12+5+13=30 units Area =1/2*perpedicular*base =1/2*12*5=30 sq units Hence may not agree to u. Your given problem bears multiple sets of answer. I only have given one. Plz comment if I am wrong

@PreMath

Ай бұрын

Hello dear, we are dealing with a special 30-60-90 triangle. I really appreciate and value your comment. Thanks for the feedback ❤️

@LuisdeBritoCamacho

Ай бұрын

Unfortunately there is only one single answer for a Triangle (30º ; 60º ; 90º)

Nếu chỉ cho số đo của 2 góc, mà không cho số đo bất kì cạnh nào thì ko thể có đáp án cụ thể được

What ? 🤔 I found AB = 8 ; BC = 6 ; AC = 10 and so the perimeter 8+6+10 = 24 and the area 8*6/2 = 24 too... No ? Ah, i think i found my error, i dont respect the angles of 30° and 60°

@PreMath

Ай бұрын

No worries. We are all lifelong learners. Thanks for sharing ❤️

Let's do it!! 1) Triangle [ABC] is (30º - 60º - 90º) 2) AB = X ; BC = Y ; AC = Z 3) Prove : (X * Y) / 2 = (X + Y + Z) ; (X * Y ) = 2X + 2Y + 2Z 4) sin(60º) = X / Z ; X = Z * sin(60º) ; X = Z * sqrt(3)/2 ; X = 0,866*Z 5) cos(60º) = Y / Z ; Y = Z * cos(60º) : Y = Z / 2 6) X * Y = (Z*sqrt(3)/2) * (Z/2) ; X * Y = (Z^2 * (sqrt(3) / 4) ; X * Y = 0,433*Z^2 sq un 7) 2 * (X + Y + Z) = 2 * (0,866*Z + (Z/2) + Z) = (Z*sqrt(3)) + Z + 2Z = (Z*sqrt(3)) + 3Z 8) 0,433*Z^2 = 3Z + Z*sqrt(3) 9) 0,433*Z^2 = 3Z + 1,732Z 10) 0,433*Z^2 = 4,7321*Z 11) Z = 10,9286 lin un 12) X = 0,866*Z = 0,866 * 10,9286 = 9,4642 lin un 13) Y = Z / 2 = 10,9286 / 2 = 5,4643 lin un 14) Check. 15) A = X * Y / 2 = 25, 8576 sq un 16) P = 10,9286 + 9,4642 + 5,4643 = 25,8571 lin un 17) Answer : BC = 5,4643 Linear Units; AB = 9,4642 Linear Units ; AC = 10,9286 Linear Units.

@PreMath

Ай бұрын

Thanks for sharing ❤️ Thanks for the feedback ❤️

AB is 6 BC is 8 AC is 10

@nandisaand5287

15 күн бұрын

That's not a 30-60-90 triangle

@yvjanard

13 күн бұрын

​​@@nandisaand5287how do you say that? 3 4 5 and 6 8 10 both form 30 60 90

@nandisaand5287

13 күн бұрын

@@yvjanard My calculator says a 3/4/5 triangle is 37°/53°/90°.

@nandisaand5287

13 күн бұрын

@@yvjanard My calculator says a 3/4/5 triangle is 37°/53°/90°.

Teacher. No soluation ..there are many similars triangular

Chu vi ko bằng diện tích đc

You didn’t tell us the perimeter or area in the end just the side lengths🙄

@PreMath

Ай бұрын

A=P=8√3+12😀

@quigonkenny

Ай бұрын

AB = 2√3 + 6 BC = 2√3 + 2 CA = 4√3 + 4 P = (2√3+6) + (2√3+2) + (4√3+4) P = 8√3 + 12 ✓ A = (2√3+6)(2√3+2)/2 A = (12+4√3+12√3+12)/2 A = (24+16√3)/2 = 8√3 + 12 ✓

1$t 🪟 View

@PreMath

Ай бұрын

Thanks dear ❤️ You are the best!