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Question

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The area of a rhombus is 120 cm2 and one of its diagonals is 24 cm. Each side of the rhombus is
(a) 10 cm
(b) 13 cm
(c) 12 cm
(d) 15 cm

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Solution

(b) 13 cm



Let ABCD be a rhombus whose diagonals AC and BD intersect at a point O.Let the length of the diagonal AC be 24 cm.Area of the rhombus=12×AC×BD cm2But the area of the rohmbus is 120 cm2 (given)12×AC×BD = 120or 12×24×BD = 120or 12×BD = 120or BD = 12012 = 10 cm OB = BD2 = 102 = 5 cm

And OA = AC2 = 242 = 12 cmNow, in right triangle AOB: AB2 = OA2 + OB2or AB2 = 122 + 52 = 144 + 25 = 169or AB = 169 = 13 cmTherefore, each side of the rhombus is 13 cm.

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