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What is the perimeter of a rhombus if the area of the rhombus is 840 cm2 and length of one of the diagonal is 2 cm more than the other diagonal?

What is the perimeter of a rhombus if the area of the rhombus is 840 cm2 and length of one of the diagonal is 2 cm more than the other diagonal? Correct Answer 116 cm

Suppose the length of a diagonal is ‘x’ cm then the length of other diagonal will be ‘x + 2’ cm;

We know that:

Area of a Rhombus = 1/2 × (Product of diagonals)

∴ 840 = 1/2 × x × (x + 2)

⇒ 1680 = x2 + 2x

⇒ x2 + 2x – 1680 = 0

⇒ (x – 40) (x + 42)

⇒ x = 40 or -42

∴ Length of a diagonal = 40 cm

Length of another diagonal = 40 + 2 = 42 cm

We know that the diagonals of a rhombus bisect each other at right angle.

∴ (Side)2 = (d12 + d22)/4

⇒ (Side)2 = (1600 + 1764)/4

⇒ (Side)2 = 841

⇒ Side = 29 cm

∴ Perimeter of a rhombus = 29 × 4 = 116 cm

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