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

Given:

The height of a right triangle is $7\ cm$ less than its base. The hypotenuse is $13\ cm$.

To do:

We have to find the other two sides.

Solution:

Let the length of the base be $x\ cm$.

The height of the triangle $=x-7\ cm$

Using the Pythagoras theorem,

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

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

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

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

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

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

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

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

$x=12$ or $x=-5$

Length cannot be negative. Therefore,

$x=12\ cm$

$x-7=12-7=5\ cm$

The length of the base is $12\ cm$ and the height of the triangle is $5\ cm$.