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in Triangles by (65.5k points)

The diagonals of a rhombus measure 16 cm and 30 cm. Find its perimeter.

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PQRS is a rhombus. The diagonals are PQ & RS.

PQ = 30 cms RS = 16 cms

According to fig In Rhombus the diagonals bisect

Each other. 

∴ PQ & RS bisect at O.

PO = OQ 

SO = OR

Considering the ∆ POR

PR2 = PO2 + OR2

= 152 + 82

= 225 + 64 = 289

∴ PR = \(\sqrt{289}\) = 17cms

∴ The perimeter of the rhombus = 4 × side PR

= 4 × 17 = 68 cms

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