Sum

If length of a diagonal of a rhombus is 30 cm and its area is 240 sq cm, find its perimeter.

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#### Solution

Let the other diagonal be d cm

Area of a rhombus = `1/2` (product of diagnols)

⇒ 240 = `1/2 xx` (30 x d)

⇒ d = `(240 xx 2)/30` = 16

AC = 30 cm

DB = 16 cm

Diagonals of a rhombus bisect at right angles.

In Δ AOB,

AO² + OB² = AB²

⇒ 15² + 8² = AB²

⇒ AB² = 225 + 64 = 289

⇒ AB = √289 = 17 cm

Thus, the side of the rhombus = 17 cm

Perimeter = `4 xx 17` = 68 cm

Concept: Area of a Rhombus

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