Question

The altitude drawn to the base of an isosceles triangle is 8, and the perimeter is 32. The area of the triangle is:

• A. $56$
• B. $48$
• C. $40$
• D. $32$

Answer 1

The correct option is B $48$

Altitude of the isosceles triangle = 8

Let equal side be a.

$\therefore$ Perimeter of the triangle = 32

$2a+b=32a+\frac{b}{2}=16-----\left(1\right)a^2-\frac{b^2}{4}=8^2(a+\frac{b}{2})(a-\frac{b}{2})=6416(a-\frac{b}{2})=64a-\frac{b}{2}=4------\left(2\right)\left(1\right)-\left(2\right),⟹b=12$

$\therefore$ Base of the triangle is = 12

$\therefore$ Area of the triangle is = $\frac{1}{2}\left(base\right)\left(height\right)=\frac{1}{2}\left(12\right)\left(8\right)=48$