Find the length of the hypotenuse of an isosceles right-angled triangle whose area is 200 cm2.

Solution:

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

Therefore,

Area of the triangle $=\frac{1}{2} \times$ base $\times$ height $=\frac{1}{2} \times a \times a=\frac{1}{2} a^{2}$

Further, given that area of isosceles right triangle = 200 cm2

$\Rightarrow \frac{1}{2} a^{2}=200$

$\Rightarrow a^{2}=400$

or, $a=\sqrt{400}=20 \mathrm{~cm}$

In an isosceles right triangle, two sides are equal ('a') and the third side is the hypotenuse, i.e. 'c' 

Therefore, $c=\sqrt{a^{2}+a^{2}}$

$=\sqrt{2 a^{2}}$

$=a \sqrt{2}$

$=20 \times 1.41$

$=28.2 \mathrm{~cm}$

Perimeter of the triangle $=a+a+c$

$=20+20+28.2$

= 68.2 cm

The length of the hypotenuse is 28.2 cm and the perimeter of the triangle is 68.2 cm.