Question

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

Answer 1

Suppose the length of the two legs of the right triangle are a cm and a cm.
Then, by Pythagoras theorem:
$$\begin{gathered} a^2+a^2=50 \\ \Rightarrow 2a^2=50 \\ \Rightarrow a^2=25 \\ \Rightarrow a=\sqrt{25} \\ \Rightarrow a=5 \end{gathered}$$

Hence, the length of each leg is 5 cm.