Question

The base and height of a triangle are in the ration $3:4$ and its area is $216c{m}^2$. The height of the triangle is

$\left(a\right)16cm\left(b\right)24cm\left(c\right)21cm\left(d\right)28cm$

Answer 1

Correct Option is (a) $16cm$

Let assume base $=3x$

Height $=4x$

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

$=\frac{1}{2}\times 3x\times 4x=6x^2$

Area $=96c{m}^2$

$6x^2=96$

$x^2=\frac{96}{6}=16$

$\Rightarrow x=4$

Base $=3\times 4=12cm$

Height $=4\times 4=16cm$