Question

The square of the hypothenuse of a right-angled isosceles triangle is $128$m. Find the length of the sides.

Answer 1

Find the length of the sides:

Let $ABC$ is an isosceles right-angled triangle in which $AB=BC=a$(equal sides) and $AC$ is the hypotenuse.

It is given that the square of the hypotenuse is $128$.

Now, In $∆ABC$ applying Pythagoras Theorem -

$\Rightarrow$${\left(AC\right)}^2={\left(AB\right)}^2+{\left(BC\right)}^2$

$\Rightarrow$ $128={\left(a\right)}^2+{\left(a\right)}^2$

$\Rightarrow$ $2a^2=128$

$\Rightarrow$ $a^2=64$

$\Rightarrow$ $a=$$\sqrt{64}$

$\Rightarrow$ $a=8cm$

Thus, the length of the required sides will be $8cm$.