Question

The base of an isosceles triangle measures 80 cm and its area is 2 `360 . cm^2` Find the perimeter of the triangle.

Answer 1

Given:

Base = 80 cm

Area = 360  

Area of an isosceles triangle=`(1/4 bsqrt(4a^2-b^2))` 

⇒`360=1/4xx80sqrt(4a^a-80^2)`  

⇒`360=20sqrt(4a^2-6400)` 

⇒`18=2sqrt(a^2-1600)` 

⇒`9=sqrt(a^2-1600)` 

Squaring both the sides, we get: 

⇒`81=a^2-1600` 

⇒`a^2=1681`  

⇒`a=41cm` 

Perimeter=`(2a+b)` 

=`[2(41+80)]=82+82=162cm`  

So, the perimeter of the triangle is 162 cm.