Question

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

Answer 1

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

Area of triangle $=96c{m}^2$

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

$\Rightarrow 12x^2=96\times 2$

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

$\Rightarrow x^2=16$

$\Rightarrow x=\sqrt{16}$

$\Rightarrow x=4cm$

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

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