Question 5 Write True or False and justify your answer:
If the side of a rhombus is 10cm and one diagonal is 16 cm, then area of the rhombus is 96 cm2.
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True Given, side of a rhombus PQRS is 10cm and one of the diagonal is 16cm. i.e., PQ = QR = RS = SP = 10cm and PR = 16cm
InΔPOQ,PQ2=OP2+OQ2[by Pythagoras theorem] [since, the diagonal of rhombus bisects each other at 90∘] ⇒OQ2=PQ2−OP2=(10)2−(8)2 ⇒OQ2=100−64=36 ⇒OQ=6m [taking positive square root because length is always positive] ∴SQ=2×OQ=2×6=12cm ∴Area of the rhombus =12 (Product of diagonals) =12(SQ×PR)=12×12×16=96cm2