Question

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

Answer 1

Let the base be $x$ cm. Then the altitude will be $x-7$ cm.

By Pythagoras theroem,

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

$\Rightarrow x^2+x^2-14x+49=169$

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

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

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

$\Rightarrow x(x-12)+5(x-12)=0$

$\Rightarrow (x+5)(x-12)=0$

$\Rightarrow x=12,-5$

Length cannot be negative, then the base is $12cm$ and the height is $5cm$