Question

Find the length of the hypotenuse of an isosceles right-angled triangle whose area is `200^2` cm . Also, find its perimeter

Answer 1

In a right isosceles triangle, base = height = a

Therefore, 

`Area of a triangle=1/2xxbasexxheight=1/2xxaxxa=1/2a^2` 

Further, given that area of isosceles right triangle=`200cm^2` 

⇒`1/2a^2=200` 

⇒`a^2=400` 

Or,` a=sqrt400=20cm`  

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(2a^2)` 

=`asqrt2`  

=`20xx1.41` 

=`28.2 cm` 

Perimeter of the triangle=` a+a+c` 

=`20+20+28.2` 

=`68.2cm` 

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