Question

In a right angled triangle the length of hypotenuse is $15$ and the difference between the other sides is $3$, then find the length of the sides.

Answer 1

Let the length of the other two sides of the right-angled triangle be $a,a+3$.

Then by the problem,

$a^2+(a+3{)}^2={15}^2$

or, $2a^2+6a+9=225$

or, $a^2+3a-108=0$

or, $a^2+12a-9a-108=0$

or, $(a-9)(a+12)=0$

or, $a=9$ [ Since $a$ is always $>0$].

So the sides of the triangle are $9,12,15$.