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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 $6\ cm$.
Updated on: 10-Oct-2022
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