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The area of a rhombus is $384\ m^2$ and one of its diagonals is $24\ m$. What is the perimeter of the rhombus?
Given:
The area of a rhombus is $384\ m^2$ and one of its diagonals is $24\ m$.
To do:
We have to find the perimeter of the rhombus.
Solution:
Let $d_1$ and $d_2$ be the two diagonals of a rhombus.
Then, $d_1=24\ m$
We know that,
Area of Rhombus $=\frac{d_1\times d_2}{2}$
$384=\frac{(24)(d_2)}{2}$
$d_2=32$
Side of the rhombus $s=\sqrt{(\frac{d_1}{2})^2+(\frac{d_2}{2})^2}$
$=\sqrt{(\frac{24}{2})^2+(\frac{32}{2})^2}$
$=\sqrt{(12)^2+(16)^2}$
$=\sqrt{144+256}$
$=\sqrt{400}$
$=20\ m$
Perimeter $=4\times s$
$=4\times20\ m$
$=80\ m$
The perimeter of the rhombus is 84 m.
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