Question

What is the perimeter of a rhombus whose diagonals are $16$ and $30$?

Answer 1

Determine the perimeter of the rhombus.

Given a rhombus of diagonal, $p=16\mathrm{unit}\mathrm{and}q=30\mathrm{unit}$.

The formula for the perimeter of the rhombus is as follows:

$P=2\sqrt{p^2+q^2}$,

where $p,q$ are the diagonals of the rhombus.

The perimeter of the rhombus is calculated as follows:

$$\begin{gathered} \begin{array}{rcl}P& =& 2\sqrt{{16}^2+{30}^2}\\ & \Rightarrow & P=2\sqrt{256+900}\\ & \Rightarrow & P=2\sqrt{1156}\\ & \Rightarrow & P=2\times 34\end{array} \\ \begin{array}{rcl}& \Rightarrow & P=68\mathrm{unit}\end{array} \end{gathered}$$

Hence, the perimeter of the rhombus is $68\mathrm{unit}.$