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Diagonals PR and QS of a rhombus PQRS are 20 cm and 48 cm respectively. Find the length of side PQ.

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i. PQRS is a rhombus. [Given] 

PR = 20 cm and QS = 48 cm [Given] 

∴ PT = (1/2) PR [Diagonals of a rhombus bisect each other] 

= (1/2) x 20 = 10 cm 

Also, QT = QS [Diagonals of a rhombus bisect each other] 

= (1/2) x 48 = 24 cm

ii. In ∆PQT, ∠PTQ = 90° [Diagonals of a rhombus are perpendicular to each other] 

∴ PQ2 = PT2 + QT2 [Pythagorastheorem] 

= 102 + 242 = 100 + 576 

∴ PQ2 = 676 

∴ PQ = √676 [Taking square root of both sides] 

= 26 cm 

∴ The length of side PQ is 26 cm.

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