Question

The perimeter of an isosceles triangle is 32 cm. The ratio of the equal side to its base is 3:2.
Find the area of the triangle.

Answer 1

Perimeter of an isosceles triangle = 32 cm

Ratio = 3 : 2

From the given ratio we get, a = 3x,

b = 3x and c = 2x

Now we can write,

3x + 3x + 2x = 32

Therefore, 8x = 32

x = 4 cm

Sides of triangle are a = 12 cm, b = 12 cm, c = 8 cm

Semi perimeter (s) $=\frac{12+12+8}{2}=16$

s = 16 cm

Area of the triangle $=\sqrt{s(s-a)(s-b)(s-c)}$

$=\sqrt{16(16-12)(16-12)(16-8)}$

$=\sqrt{16\times 4\times 4\times 8}$

$=32\sqrt{2}c{m}^2$