Question

The diagonals of a rhombus are 8 cm and 15 cm. Find its side.

Answer 1

Given, AC = 15 cm, BD = 8 cm.

OA = OC = $\frac{15}{2}$

OB = OD = $\frac{8}{2}$

Since, the diagonals of a rhombus bisect each other at ${90}^{\circ }$, therefore in the $\Delta AOB$, we have
$A{B}^2=O{A}^2+O{B}^2$
$\Rightarrow A{B}^2={\left(\frac{15}{2}\right)}^2+{\left(\frac{8}{2}\right)}^2=(7.5{)}^2+(4{)}^2=56.25+16$
$\Rightarrow A{B}^2=72.25$
$\Rightarrow AB=\sqrt{72.25}$
$\Rightarrow AB=8.5cm$
Since it is a rhombus, the length of each side is 8.5 cm.