Question

The length of the base of a triangle is 4 cm smaller than the length of the altitude, and the area of the triangle is 96 $c{m}^2$. Find. the lengths of the base and the altitude of the triangle.

Answer 1

if the base is assumed to be $b$ then the altitude is $h=b+4$.

given area of the triangle is 96.

$\frac{1}{2}b(b+4)=96$

$⟹b^2+4b-192=0$

Solving this quadratic equation for the positive value, we get, $b=12cm$ and hence $h=16cm$