Question

The square of the hypotenuse of a right–angled isosceles triangle is 288cm. Find the length of the legs.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{ABC}\mathrm{be}\mathrm{an}\mathrm{isosceles}\mathrm{right}\mathrm{angled}∆,\mathrm{in}\mathrm{which}\angle \mathrm{B}=90° \\ \mathrm{Now},\mathrm{AB}=\mathrm{BC}. \\ \mathrm{now},{\mathrm{AC}}^2={\mathrm{AB}}^2+{\mathrm{BC}}^2\left[\mathrm{Pythagoras}\mathrm{Theorem}\right] \\ \Rightarrow 288={\mathrm{AB}}^2+{\mathrm{AB}}^2 \\ \Rightarrow 2{\mathrm{AB}}^2=288 \\ \Rightarrow {\mathrm{AB}}^2=144 \\ \Rightarrow \mathrm{AB}=12\mathrm{cm} \\ \mathrm{Now},\mathrm{equal}\mathrm{legs}\mathrm{of}∆\mathrm{ABC}\mathrm{are}\mathrm{AB}=\mathrm{BC}=12\mathrm{cm} \end{gathered}$$