Question

The altitude of a right triangle is $7cm$ less then its base. If the hypotenuse is $13cm$, find the other two sides.

Answer 1

Let $x$ be the base of the triangle, then the altitude will be $\left(x-7\right)$.

By Pythagoras theorem,

$x^2+{\left(x-7\right)}^2={\left(13\right)}^2$

$2x^2-14x+49-169=0$

$2x^2-14x-120=0$

$x^2-7x-60=0$

$x^2-12x+5x-60=0$

$\left(x-12\right)\left(x+5\right)=0$

$x=12,x=-5$

Since the side of the triangle cannot be negative, so the base of the triangle is $12cm$ and the altitude of the triangle will be $12-7=5cm$.