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Question
Lengths of diagonals of a rhombus ABCD are 16 cm and 12 cm. Find the side and perimeter of the rhombus.
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Solution
ABCD is a rhombus.
Here, segment AC and segment BD are the diagonals of the rhombus ABCD.
l(AC) = 16 cm and l(BD) = 12 cm.
Diagonals of a rhombus are perpendicular bisectors of each other.
∴ m∠AOD = 90°
Also, l(OA) = `1/2l(AC) = 1/2 xx 16 = 8 cm`
l(OD) = `1/2l(BD) = 1/2`× 12 = 6 cm
In right ∆AOD,
l(AD)2 = l(OA)2 + l(OD)2 ...[Pythagoras theorem]
⇒ l(AD)2 = (8)2 + (6)2
⇒ l(AD)2 = 64 + 36 = 100
⇒ l(AD) = \[\sqrt{100}\] = 10 cm
All sides of a rhombus are equal.
∴ Perimeter of the rhombus ABCD = 4 × Side of a rhombus = 4 × 10 = 40 cm
Thus, the side and perimeter of the rhombus are 10 cm and 40 cm, respectively.
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