Question

If the sides of a triangle are 3 cm, 4 cm and 6 cm long, determine whether the triangle is right-angled triangle.

Answer 1

$$\begin{gathered} \mathrm{In}\mathrm{the}\mathrm{given}\mathrm{triangle},\mathrm{the}\mathrm{largest}\mathrm{side}\mathrm{is}6\mathrm{cm}. \\ \mathrm{We}\mathrm{know}\mathrm{that}\mathrm{in}\mathrm{a}\mathrm{right}-\mathrm{angled}\mathrm{triangle},\mathrm{the}\mathrm{sum}\mathrm{of}\mathrm{the}\mathrm{squares}\mathrm{of}\mathrm{the}\mathrm{smaller}\mathrm{sides}\mathrm{should}\mathrm{be}\mathrm{equal}\mathrm{to}\mathrm{the}\mathrm{square}\mathrm{of}\mathrm{the}\mathrm{largest}\mathrm{side}. \\ \mathrm{Therefore}, \\ {3}^2+4^2=9+16=25 \\ \mathrm{But}, \\ {6}^2=36 \\ \Rightarrow 3^2+4^2\ne 6^2 \\ \mathrm{Hence},\mathrm{the}\mathrm{given}\mathrm{triangle}\mathrm{is}\mathrm{not}\mathrm{a}\mathrm{right}-\mathrm{angled}\mathrm{triangle}. \end{gathered}$$