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.

• A. $30\sqrt{2}c{m}^2$
• B. $32\sqrt{2}c{m}^2$
• C. $35\sqrt{2}c{m}^2$
• D. $40\sqrt{2}c{m}^2$

Answer 1

The correct option is B

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

Ratio of the equal side to the base of an isosceles triangle is 3 : 2, Let the sides be 3x, 3x and 2x.

perimeter of triangle $=3x+3x+2x=8x$

Given perimeter of the triangle = 32m
$\therefore 8x=32;x=\frac{32}{8}=4$

So, the sides of the isosceles triangle are $(3\times 4)cm$, $(3\times 4)cm$, $(2\times 4)cm$, i.e., $12cm,12cm$ and $8cm$.

$\therefore s=\frac{12+12+8}{2}=\frac{32}{2}=16cm$

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

$=\sqrt{16\times 4\times 4\times 8}=\sqrt{4\times 4\times 4\times 4\times 4\times 2}$

$=4\times 4\times 2\sqrt{2}=32\sqrt{2}c{m}^2$