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Question
Diagonals PR and QS of a rhombus PQRS are 20 cm and 48 cm respectively. Find the length of side PQ.
Solution
Diagonals of a rhombus bisect each other at right angles.
PR = 20 cm, QS = 48 cm
⇒ `"PO" = 1/2 "PR"`
= `1/2 xx 20`
= 10 cm
Similarly, QS = 48 cm
⇒ `"QO" = 1/2 "SQ"`
= `1/2 xx 48`
= 24 cm
In ΔPOQ, applying Pythagoras theorem,
OQ2 + QP2 = PQ2
⇒ 242 + 102 = PQ2
⇒ PQ2 = 576 + 100
⇒ PQ2 = 676
⇒ PQ = 26 cm
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