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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 $24\ cm^2$.