A triangle has sides $5(k-2)$ cm, $12(k-2)$ cm and $13(k-2)$ cm, where $k2$. Prove

Question

A triangle has sides $5(k-2)$ cm, $12(k-2)$ cm and $13(k-2)$ cm, where $k>2$. Prove it is right-angled. If its perimeter is $150$ cm, find its area.

Accepted Answer

(a) right-angled by the converse theorem; (b) $750\text{ cm}^2$.

An algebraic 5–12–13 triangle