Question

The area of a right-angled triangle is \[96\ \text{m}^{2}\]. If its base is three times its altitude, find the base.

Answer 1

Let the altitude of the triangle be $$h\text{ m}$$. 

Then, the base of the triangle is $$b = 3h\text{ m}$$.

Area of a right-angled triangle $$= \frac{1}{2} \times \text{base} \times \text{altitude}$$.

$$\frac{1}{2} \times 3h \times h = 96$$ 

$$\frac{3}{2} h^2 = 96$$

$$h^2 = \frac{96 \times 2}{3} = 64$$

$$h = 8\text{ m} \quad [\because h > 0]$$ 

Base of the triangle $$= 3h$$

$$= 3 \times 8$$

$$= 24\text{ m}$$