Question

an architectural firm wants to replicate a nearby estate with some changes. the new estate will be larger than the original by a scale factor of 1:10. a section of the roof in the original estate is constructed using 45 - 45 - 90 triangles. the hypotenuse of the triangle is 10 meters long. what will be the length of the triangle legs for the larger estate? 100.00 m 14.14 m 70.71 m 141.42 m

Explanation:

Step1: Recall 45 - 45 - 90 triangle property

In a 45 - 45 - 90 triangle, if the hypotenuse is $c$ and the legs are $a$ and $b$ (where $a = b$), then $c=a\sqrt{2}$. For the original triangle with $c = 10$ meters, we can find the length of the leg of the original triangle. So, $a=\frac{c}{\sqrt{2}}=\frac{10}{\sqrt{2}} = 5\sqrt{2}$ meters.

Step2: Apply the scale - factor

The scale factor is 1:10. To find the length of the leg of the larger triangle, we multiply the length of the leg of the original triangle by 10. The length of the leg of the larger triangle $A=10\times5\sqrt{2}=50\sqrt{2}\approx70.71$ meters.

Answer:

70.71 m