Question

The two legs of a right triangle are equal and the square of the hypotenuse is 50. Find the length of each leg.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{length}\mathrm{of}\mathrm{each}\mathrm{leg}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{triangle}\mathrm{be}\mathrm{x}\mathrm{units}. \\ \mathrm{Using}\mathrm{the}\mathrm{Pythagoras}\mathrm{theorem},\mathrm{we}\mathrm{get}: \\ {\mathrm{x}}^2+{\mathrm{x}}^2=(\mathrm{Hypotenuse}{)}^2 \\ {\mathrm{x}}^2+{\mathrm{x}}^2=50 \\ 2{\mathrm{x}}^2=50 \\ \Rightarrow {\mathrm{x}}^2=25 \\ \Rightarrow \mathrm{x}=5 \\ \mathrm{Hence},\mathrm{we}\mathrm{can}\mathrm{say}\mathrm{that}\mathrm{the}\mathrm{length}\mathrm{of}\mathrm{each}\mathrm{leg}\mathrm{is}5\mathrm{units}. \end{gathered}$$