Question

Find the lenght of the hypotenuse of an isosceles right-angled triangle whose area is 200 $c{m}^2$. Also, find its perimeter. [Given, $\sqrt{2}$ = 1.41.]

Answer 1

In an isosceles triangle,any two sides are equal.So,in this question, base=height or (b=h)

Area of ∆ =$\frac{1}{2}\times b\times h$

$200=\frac{1}{2}\times b^2$

$400=b^2$

$b=\sqrt{400}=20$

So, b=h=20

Hypotenuse $=\sqrt{400+400}=20\sqrt{2}=20\times 1.414=28.28$

Perimeter = 20 + 20 + 28.28 = 68.28 cm