Question

The two legs of a right triangle are equal and the square of the hypotenuse is $50$. Find the length of each leg.

Answer 1

$AB=BC$ [Given]

$(AC{)}^2=50$

Let $AB=x$

$\therefore$ Applying Pythagoras Theorem

$(AC{)}^2=(AB{)}^2+(BC{)}^2$

$50=x^2+x^2$

$50=2x^2$

$\therefore x^2=25$

$x=\sqrt{25}$

$\therefore x=5$

$\therefore AB=BC=5units$

and $AC=\sqrt{50}units$