Question

In a right-angled triangle the hypotenuse is of $13$ cm and the difference between the other sides is $7$ cm, then find the two sides.

Answer 1

Let one of the other sides be $x$ then the other side is $x+7$.

Then according to the problem,

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

or, $2x^2+14x-120=0$

or, $x^2+7x-60=0$

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

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

or, $x=5$. [ Since $x\ne -12$]

So the other sides are $5$ cm and $5+7=12$ cm.