Question

An isosceles right triangle has an area of $200c{m}^2$. What is the length of its hypotenuse?

Answer 1

In an isosceles right angled triangle, the two sides on the right angle are equal

Let the equal side be aa

Hence, hypotenuse of the isosceles right-angled triangle of side $a=\sqrt{a^2+a^2}=\sqrt{2}a$

In the isosceles right triangle, the base and height$=a$

Hence, area of the triangle$=\frac{1}{2}\times base\times height=$

$\frac{1}{2}\times a\times a=200$ sq cm

$=>a^2=400$

$=>a=20cm$

And the hypotenuse$=\sqrt{2}a=20\sqrt{2}cm$