Question

Length of diagonals of a rhombus $ABCD$ are $16cm$ and $12cm$. Find the side and perimeter of the rhombus.

Answer 1

Let $pandq$ be the diagonals and $a$ be the side of rhombus,

$p=16cm,q=12cm$

As we know in a rhombus, each side is of same length and side can be calculated as below when lengths of diagonal are given-

$a=\frac{\sqrt{p^2+q^2}}{2}$

$a=\frac{\sqrt{{16}^2+{12}^2}}{2}$

$a=\frac{\sqrt{256+144}}{2}$

$a=\frac{\sqrt{400}}{2}$

$a=\frac{20}{2}$

$a=10cm$

Perimeter of rhombus $=4a=4\times 10=40cm$

Hence, the perimeter of rhombus $ABCD$ is $40cm.$