Question

The sides of a right angled triangle containing the right angle are $5cm$ and $12cm$, find its hypotenuse.

Answer 1

Let $AB$ and $BC$ be the sides of the triangle containing right angle and $AC$ be the hypotenuse as shown in the above figure:

It is given that $AB=5$ cm $BC=12$ cm

According to the pythagoras theorem

$A{C}^2=A{B}^2+B{C}^2\Rightarrow A{C}^2=5^2+{12}^2\Rightarrow A{C}^2=25+144\Rightarrow A{C}^2=169\Rightarrow AC=\sqrt{169}\Rightarrow AC=13$

Hence, the hypotenuse $AC=13$ cm.