Question

In the rhombus, AC=24 and BD=32. Find the perimeter of the rhombus

Answer 1

Given: The diagonals of a rhombus as shown in the image

To Determine: The perimeter of the rhombus

Solution

The perimeter of a rhombus can be calculated if the diagonals are given by the formula below

$\begin{gathered} P=2\sqrt{a^2+b^2} \\ P=Perimeter \\ a=diagonal1 \\ b=diagonal2 \end{gathered}$

Substitute the given diagonals into the formula

$\begin{gathered} AC=24 \\ BD=32 \\ P=2\sqrt{24^2+32^2} \\ P=2\sqrt{576+1024} \\ p=2\sqrt{1600} \\ P=2\times40 \\ P=80 \end{gathered}$

Hence, the perimeter is 80