Question

The hypotenuse of a right-angled triangle is $4m$. If its other sides are equal, find the length of each side.

Answer 1

Step 1: Find the length of each side

Given, the hypotenuse of a right-angled triangle $=4m$

and other sides are equal

Let a right-angled $△ABC$ such that

$AB=BCandhypotenuseAC=4m$

By the Pythagoras theorem, we have

$$\begin{gathered} A{C}^2=A{B}^2+B{C}^2 \\ \Rightarrow 4^2=A{B}^2+A{B}^2 \\ \Rightarrow 16=2A{B}^2 \\ \Rightarrow A{B}^2=\frac{16}{2}=8 \\ \Rightarrow AB=\sqrt{8}=2\sqrt{2} \end{gathered}$$

So, $AB=BC=2\sqrt{2}m$

Hence, the length of the other sides is $2\sqrt{2}m$.