Question

The hypotenuse of an isosceles
right angled triangle is
$\sqrt{242}$
cm. Find
the length of each equal side.​

Answer 1

$\star\:\:\:\bf\large\underline\blue{Question:-}$

• The hypotenuse of an isosceles is $\sqrt{242}$cm. Find the length of each side.

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Let each equal side measures $x\:cm$

Therefore, by Pythagoras Theorem,

$AC^{2}=AR^{2}+RC^{2}$

Putting the values, we get,

$( \sqrt{242})^{2} = {x}^{2} + {x}^{2}$

$\implies 242 = 2 {x}^{2}$

$\implies {x}^{2} = \frac{242}{2}$

$\implies {x}^{2} = 121$

$\implies x = \pm11cm$

Since, lengths of sides cannot be negative, therefore,

$x = 11cm$

$\star\:\:\:\bf\large\underline\blue{Answer:-}$

• Length of each equal sides of the given right angle isosceles triangle is 11cm.