The side of a rhombus are 5 cm each and one diagonal is 8 cm. Calculate the length of the other diagonal and the area of the rhombus.

Given: The side of a rhombus are 5 cm each and one diagonal is 8 cm.

To do: To calculate the length of the other diagonal and the area of the rhombus.

Solution: 

As given Length of diagonal of the rhombus $d_2=8\ cm$

Length of the side of the rhombus $=5\ cm$

Diagonals bisect each other and they are perpendicular in rhombus, Let half of the length of second diagonal be $x$. As two diagonals and a side form right angled triangle.

$\Rightarrow x^2+4^2=5^2$

$\Rightarrow x^2=25-16$

$\Rightarrow x^2=9$

$\Rightarrow x=\sqrt{9}$

$\Rightarrow x=3$

$\Rightarrow$Length of second Diagonal $d_2=2x=6\ cm$

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

$=\frac{1}{2}\times8\times6$

$=24\ cm^2$

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

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Updated on: 10-Oct-2022

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