Question

The longest side of a right-angled triangle is $5cm.$ If one of the other two sides is $4cm,$then find the length of the third side.

Answer 1

Let the length of the third side be $x$

By Pythagoras theorem

The square on the hypotenuse is equal to the sum of the squares on the other two sides.

$$\begin{gathered} 5^2=4^2+x^2 \\ \Rightarrow 25=16+x^2 \\ \Rightarrow 25-16=x^2 \\ \Rightarrow 9=x^2 \\ \Rightarrow x=\sqrt{9} \\ \Rightarrow x=3cm \end{gathered}$$

Hence, the length of the third side is $3cm.$