Question

A right angle triangle has hypotenuse of length $pcm$ and one side of length $qcm.$ If $p-q=1$, find the length of the third side of the triangle.

Answer 1

Let the third side be x cm. then, by pythagoras theorem, we have

$p^2=q^2+x^2$

$\Rightarrow$ $x^2=p^2-q^2=(p-q)(p+q)=p+q$ [$\because p-q=1$]

$\Rightarrow$ $x=\sqrt{p+q}=\sqrt{2q+1}$ [$\because p-q=1\therefore p=q+1$]

Hence, the length of the third side is $\sqrt{2q+1}cm$.