Question

The base and height of $\Delta$ are in ratio $3:4$ and its area is $96{\text{cm}}^2$, then find its base and height.

Answer 1

Let the base and height be $3x$ and $4x.$

Area of a triangle = $\frac{1}{2}\times$ base $\times$ height

$\Rightarrow \frac{1}{2}.3x.4x=96$

$\Rightarrow \frac{1}{2}.12x^2=96$

$\Rightarrow 6x^2=96$

$\Rightarrow x^2=96/6$

$\Rightarrow x^2=16$

$\Rightarrow x=\sqrt{16}$

$\Rightarrow x=4$

$\therefore Base=3x=3\times 4=12cm$

Height $=4x=4\times 4=16cm$