Question 59

The lengths of two diagonals of a rhombus are 24 cm and 32 cm. What is the side (in cm) of the rhombus?

Solution

Give : ABCD is a rhombus, AC = 24 cm and BD = 32 cm

To find : AB = ?

Solution : Diagonals of a rhombus bisect each other at right angle.

=> OA = $$\frac{24}{2}=12$$ cm and OB = $$\frac{32}{2}=16$$ cm

Thus, in $$\triangle$$ OAB,

=> $$(AB)^2=(OA)^2+(OB)^2$$

=> $$(AB)^2=(12)^2+(16)^2$$

=> $$(AB)^2=144+256=400$$

=> $$AB=\sqrt{400}=20$$ cm

=> Ans - (A)

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