Question

A right triangle has a hypotenuse of length $pcm$ and one side of length $qcm$. If $p-q=1$, find the length of the third side of the triangle if $p=5$ and $q=4$

Answer 1

In a right angled triangle, ${\text{Hypotenuse}}^2={{\text{side}}_1}^2+{{\text{side}}_2}^2$
So, $p^2=q^2+{\left({\text{side}}_2\right)}^2$
$\Rightarrow {\left({\text{side}}_2\right)}^2=p^2-q^2$
$\Rightarrow {\text{side}}_2=\sqrt{p^2-q^2}=\sqrt{(p+q)(p-q)}$
Given, $p-q=1$
Therefore, ${\text{side}}_2=\sqrt{(p+q)\times 1}=\sqrt{p+q}=3$ cm