Question

In a right angled triangle $ABC,\angle B={90}^{\circ }$.

If $AC=13cm,BC=5cm$, find $AB$

Answer 1

$△$ ABC is a right-angled triangle.

By Pythagoras theorem,

$A{C}^2=B{C}^2+A{B}^2$

$\Rightarrow {13}^2=5^2+A{B}^2$

$\Rightarrow A{B}^2=-(5{)}^2+{13}^2$

$\Rightarrow A{B}^2=-25+169$

$\Rightarrow A{B}^2=144$

$\Rightarrow AB=\sqrt{144}$

$\Rightarrow AB=12cm.$