Question 20

# The area of a rhombus is $$24m^{2}$$ and the length of one of its diagonals is 8 m. The length ofeach side of the rhombus will be:

Solution

The correct option is A.

In a Rhombus diagonals bisect each other at right angle. Let diagonal AC= 8m.Â

Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â Area of rhombus = $$\frac{1}{2}$$ $$d_{1}d_{2}$$Â

Â  Â $$\Rightarrow$$ Â 24 = $$\frac{1}{2}$$ 8$$\times d_{2}$$

Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â $$d_{2}$$ = 6mÂ

AO=4m and DO = 3 m Â so, in $$\triangle$$AOD , $$AD^{2}=AO^{2}+DO^{2}$$

Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â $$\Rightarrow$$ AD = 5mÂ
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