Question

The given figure shows a quadrilateral ABCD in which AD=13 cm, DC=12 cm, B C=3 cm and $\angle ABD=\angle BCD={90}^{\circ }$. Calculate the length of $AB.$

Answer 1

Given $AD=13cm,DC=12m$
$BC=3cm$
$\angle ABD=\angle BCD=90˚$
$BCD$ is a right triangle.
$B{D}^2=B{C}^2+D{C}^2$[Pythagoras theorem]
$B{D}^2=3^2+{12}^2$
$B{D}^2=9+144$
$B{D}^2=153$
$ABD$ is a right triangle.
$A{D}^2=A{B}^2+B{D}^2$[Pythagoras theorem]
${13}^2=A{B}^2+153$
$169=A{B}^2+153$
$A{B}^2=169-153$
$A{B}^2=16$
Taking square root on both sides,
$AB=4cm$
Hence the length of $AB$ is $4cm.$