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Question
The diagonals of a rhombus measure 16 cm and 30 cm. Find its perimeter.
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Solution
Let ABCD be a rhombus (all sides are of equal length) and its diagonals, AC and BD, are intersecting each other at point O. Diagonals in a rhombus bisect each other at 90°. It can be observed that
AO = `(AC)/2`
= `16/2`
= 8 cm
BO = `(BD)/2`
= `30/2`
= 15 cm
By applying Pythagoras theorem in ΔAOB,
OA2 + OB2 = AB2
82 + 152 = AB2
64 + 225 = AB2
289 = AB2
AB = 17
Therefore, the length of the side of rhombus is 17 cm.
Perimeter of rhombus = 4 × Side of the rhombus
= 4 × 17
= 68 cm
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