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.
