The area of a rhombus is $84\ cm^2$ and the length of the diagonal is $24\ cm$. Find the side of the rhombus.

Given: The area of a rhombus is $84\ cm^2$ and the length of the diagonal is $24\ cm$.

To do: To find the side of the rhombus.

Solution: 

Area of the rhombus $=84\ cm^2$

Length of the diagonal $d_1=24\ cm$

Let's consider the second diagonal to be $d_2$.

$\therefore$ Area of the rhombus$=\frac{1}{2}\times d_1\times d_2$

$\Rightarrow \frac{1}{2}\times 24\times d_2=84$

$\Rightarrow d_2=\frac{84\times2}{24}$

$\Rightarrow d_2=7\ cm$

Thus, the length of the second diagonal is $7\ cm$.

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Updated on: 10-Oct-2022

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