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# Find the area of a rhombus whose side is $5\ cm$ and whose altitude is $4.8\ cm$. If one of its diagonal is $8\ cm$ long, find the length of the other diagonal.

**Given:**A rhombus whose side is $5\ cm$ and whose altitude is $4.8\ cm$ and one of its diagonal is $8\ cm$ long.

**To do:**To find its area and to find the length of the other diagonal.

**Solution:**

As given, length of the side of the rhombus$=5\ cm$

Altitude$( height)$ of the rhombus$=4.8\ cm$

And diagonal of the rhombus$=8\ cm$

Area of rhombus$=$Base$\times$Height

$=5\times4.8$

$=24\ cm^2$

But Area of the rhombus$=\frac{1}{2}\times Product\ of\ diagonals$

$\Rightarrow \frac{1}{2}\times( 8\times x)=24$

$\Rightarrow 8x=48$

$\Rightarrow x=\frac{48}{8}=6\ cm$

Thus, area of the rhombus is $24\ cm^2$ and length of the other diagonal is $6\ cm$.

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