Question 72

The area of a rhombus is 216 $$cm^2$$ and the length of one of its diagonals is 24 cm. How long is each side of the rhombus?

Solution

D1 and D2 be the diagonals of the rhombus

Area of rhombus $$= \frac{1}{2} (D1 ×D2)$$

$$216= \frac{1}{2}(24 \times D2)$$

$$D2 = 18 cm$$

As we know that diagonals of a rhombus bisect each other at $$90^\circ$$

So acc phythagoras theorem,

$$side =\sqrt{12^2+9^2} = \sqrt{144 +81}= \sqrt{225} = 15 cm$$

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