The area of a rhombus is 216 cm2 and one of its diagonals measures 24 cm. Find: (i) the length of the other diagonal, (ii) the length of each of its sides, (iii) its perimeter.

Question

KnowledgeBoat · Accepted Answer

(i) Given: Area of rhombus = 216 cm2 One diagonal = 24 cm Let 'd' be the other diagonal of rhombus. Hence the length of the other diagonal = 18 cm. (ii) The rhombus is shown in the figure below: Diagonal AC = 24 cm. The diagonals of a rhombus bisect each other at right angle. Then, OA = OC = = 12 cm Diagonal, BD = 18 cm Then, OB = OD = = 9 cm Applying pythagoras theorem for △AOB, we get: ⇒ AB2 = OA2 + OB2 ⇒ AB2 = (12)2 + (9)2 ⇒ AB2 = 144 + 81 ⇒ AB2 = 225 ⇒ AB = ⇒ AB = 15 cm. Hence, the length of the each of its side = 15 cm. (iii) Perimeter of rhombus = 4 × side = 4 × 15 = 60 cm. Hence, perimeter of the rhombus = 60 cm.

Mathematics

The area of a rhombus is 216 cm² and one of its diagonals measures 24 cm. Find:
(i) the length of the other diagonal,
(ii) the length of each of its sides,
(iii) its perimeter.

Mensuration

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