Question

The base of an isosceles triangle measures 80 cm and its area is 360 cm². Find the perimeter of the triangle.

Answer 1

Given:

Base = 80 cm

Area = 360 cm²

Area of an isosceles triangle = \((\frac{1}{4}b\sqrt{4a^2-b^2})\)

Squaring both the sides, we get:

\(\Rightarrow\) 81 = a² - 1600

\(\Rightarrow\) a² = 1681

\(\Rightarrow\) a = 41 cm

Perimeter = (2a + b)

= [2(41)+80] = 82 + 80 = 162 cm

So, the perimeter of the triangle is 162 cm.