Question

A right angle triangle has hypotenuse of length $qcm$ and one side of length $pcm$. If $q-p=2$ express the length of third side of right angle triangle in terms of $q$.

Answer 1

Let $x$ be the third side of the right angle triangle.

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

$\Rightarrow x^2$ $=q^2-p^2=(q-p)(q+p)=2(q+p)(\because q-p=2)=2(q+(q-2))=4(q-1)$

$\Rightarrow x=\sqrt{4(q-1)}=2\sqrt{q-1}$

Hence the length of third side of right angle triangle in terms of $q$ is $\left(2\sqrt{q-1}\right)$.