The area of a right-angled triangle is 96 sq metres
Question:

The area of a right-angled triangle is 96 sq metres. If the base is three times the altitude, find the base.

Solution:

Let the altitude of the triangle be x m.
Therefore, the base will be 3x m.

Area of a triangle $=\frac{1}{2} \times$ Base $\times$ Altitude

$\therefore \frac{1}{2} \times 3 x \times x=96(\because$ Area $=96$ sq $\mathrm{m})$

$\Rightarrow \frac{x^{2}}{2}=32$

$\Rightarrow x^{2}=64$

$\Rightarrow x=\pm 8$

The value of $x$ cannot be negative.

Therefore, the altitude and base of the triangle are $8 \mathrm{~m}$ and $(3 \times 8=24 \mathrm{~m})$, respectively.