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Question
If the diagonals of a rhombus are 18 cm and 24 cm respectively, then its side is equal to
Options
16 cm
15 cm
20 cm
17 cm
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Solution
Let ABCD be rhombus with diagonals AC and BD 18cm and 24cm respectively.
We know that diagonals of the rhombus bisect each other at right angles.
Therefore,
`AO = 1/2 AC `
`AO = 1/2 (18cm) `
AO = 9cm
Similarly,
`BO = 1/2 BD `
`BO = 1/2(24cm)`
BO = 12cm
Also, ΔAOB is a right angled triangle.
By Pythagoras theorem, we get:
`AB^2 = AO^2 + BO^2`
`AB = sqrt(AO^2 + BO^2)`
`AB = sqrt(9^2 + 12^2)`
`AB = sqrt225`
AB = 15cm
Hence the correct choice is (b).
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