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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
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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