You can solve this without calculation when you realise that x=s/2. If you draw a square with 10 as a side you can fill it with 4 green triangles and a square with x as a side. This shows that the square with s as a side is 4/5 as big as a square with 100 as a side so the answer is 80.
Из коэффициента подобия треугольников ½ делаем два полезных вывода: во-первых, их стык находится на середине стороны квадрата, во-вторых, это также пропорция катетов (как и в большом, у которого оба на виду). Ну всё, задача, считай, решена: сторона квадрата 2*10/√5=2*2*5/√5=4√5, откуда площадь 16*5=80.
You can generalize the set-up in this problem to derive the area of the square for any pair of the lengths: Area = (b^4)/(b^2 + (b-a)^2). In this case, a = 5 and b = 10, so: Area = 10^4 / (10^2 + 5^2) = 10,000/125 = 80.
Tenemos dos triángulos de esquina, de lados: a/b/10 y c/(b-a)/c---> Razón de semejanza entre ambos triángulos =s=5/10=1/2---> (b-a)=b*s=b/2---> a=b/2 ---> b²+(b²/4)=10²=5b²/4--->b²=400/5=80 u2² Gracias y saludos
If you construct the hypotenuse of the the 5-10 triangle (draw line from upper left corner of square to lower intersection of 5 line & right side of square), this triangle is similar to the 2 other triangles & to triangle of sides 1/2/√5. So you can assign lengths starting at lower triangle's short leg & going counterclockwise: X, 2X, 2X, 4X. So X² + (2X)² = 5². X = √5 square side = 4X = 4√5. Square area = (4√5)² = 80.
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80 let the side of the square =n , and the side of the similar triangle =? Both triangles are similar then n/10 = ?/5 5/10 n =? 1/2 n=? Hence, the dimensions of largest triangle are 10, n, and 1/2n 10^2 = n^2 + 1/4 n^2 100= 5/4n^2 100 * 4/5 =n^2 80 = ANSWER
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You can solve this without calculation when you realise that x=s/2. If you draw a square with 10 as a side you can fill it with 4 green triangles and a square with x as a side. This shows that the square with s as a side is 4/5 as big as a square with 100 as a side so the answer is 80.
It’s pretty funny that I’m watching this while making my maths homework for my test Wednesday
That's actually awesome! 😎
Из коэффициента подобия треугольников ½ делаем два полезных вывода: во-первых, их стык находится на середине стороны квадрата, во-вторых, это также пропорция катетов (как и в большом, у которого оба на виду). Ну всё, задача, считай, решена: сторона квадрата 2*10/√5=2*2*5/√5=4√5, откуда площадь 16*5=80.
Отличная работа! Очень красиво и логично всё расписали. Приятно видеть такое точное и аккуратное решение. 😊
👍👍👍
You can generalize the set-up in this problem to derive the area of the square for any pair of the lengths: Area = (b^4)/(b^2 + (b-a)^2). In this case, a = 5 and b = 10, so: Area = 10^4 / (10^2 + 5^2) = 10,000/125 = 80.
Nice! That generalization works! Great job!
I’m not sure how it will relax me, but I think I see some similar triangles.
That's the first sign of relaxation! 🤣
Tenemos dos triángulos de esquina, de lados: a/b/10 y c/(b-a)/c---> Razón de semejanza entre ambos triángulos =s=5/10=1/2---> (b-a)=b*s=b/2---> a=b/2 ---> b²+(b²/4)=10²=5b²/4--->b²=400/5=80 u2²
Gracias y saludos
¡Gracias por compartir tu solución!
If you construct the hypotenuse of the the 5-10 triangle (draw line from upper left corner of square to lower intersection of 5 line & right side of square), this triangle is similar to the 2 other triangles & to triangle of sides 1/2/√5. So you can assign lengths starting at lower triangle's short leg & going counterclockwise: X, 2X, 2X, 4X. So X² + (2X)² = 5². X = √5
square side = 4X = 4√5. Square area = (4√5)² = 80.
Great job!
Draw it in autocad.
Thanks for the forecast! Just a quick off-topic question: My OKX wallet holds some USDT, and I have the seed phrase. (air carpet target dish off jeans toilet sweet piano spoil fruit essay). How can I transfer them to Binance?
8.9443×8.9443=80area
Autocad? :D
80
I have to ask. Do you have a different channel where you do math problems with your son? You sound so much like him.
Hi. Eh...no... This is the only channel that I have!
The answer is 80 but its not a square s = 10 and one side is 8
80
let the side of the square =n
, and the side of the similar triangle =? Both triangles are similar
then n/10 = ?/5
5/10 n =?
1/2 n=?
Hence, the dimensions of largest triangle are 10, n, and 1/2n
10^2 = n^2 + 1/4 n^2
100= 5/4n^2
100 * 4/5 =n^2
80 = ANSWER
What can I say: That's it!