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Question

The diagonals of a rhombus are in the ratio 2:3. Find the length of smaller diagonal, if the area of the rhombus is 27 cm2.

A
3 cm
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B
4 cm
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C
6 cm
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D
8 cm
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Solution

The correct option is C 6 cm
Given
Ratio of the diagonals = 2:3
Area of the rhombus = 27 cm2

Let the length of the smaller diagonal be 2y and the larger diagonal be 3y

Area of the rhombus
=12×(product of diagonals)

27=12×2y×3y

27=12×6y2

27=3y2

y2=273=9

y = 9 = 3

Hence, length of the smaller diagonal = 2y = 2(3) = 6 cm

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