Question

If the square of the hypotenuse of an isosceles right triangle is 125 cm square find the length of each side.​

Answer 1

,QWERTYUIOPASDFGHJKLZXCVBNMqwertyuiopasdfghjklzxcvbnm

Answer 2

$\bold\red{\underline{\underline{Answer:}}}$

$\bold{Length \ of \ sides \ are \ 7.9cm,7.9cm}$

$\bold{and \ 11.2cm \ respectively.}$

$\bold\blue{Explanation}$

In isosceles triangle two sides are of same length.

$\bold\orange{Given:}$

$\bold{Hypotenuse^{2}=125cm^{2}}$

Triangle is an isosceles right angled triangle.

$\bold\pink{To \ find:}$

Length of each side.

$\bold\green{\underline{\underline{Solution}}}$

By Pythagoras theorem

$\bold{Hypotenuse^{2}=(Side1)^{2}+(Side2)^{2}}$

The triangle is an isosceles triangle, therefore

Side1= Side2

$\bold{125=2(side)^{2}}$

$\bold{side^{2}=\frac{125}{2}}$

$\bold{side^{2}=62.5}$

On taking square root of both sides

$\bold{side=7.9cm(approx)}$

______________________________________

$\bold{Hypotenuse^{2}=125}$

On taking square root of both sides

Hypotenuse=11.2cm(approx)

Therefore,

$\bold\purple{Length \ of \ sides \ are \ 7.9cm,7.9cm}$

$\bold\purple{and \ 11.2cm \ respectively.}$