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Question
The lengths of the diagonals of a rhombus are 24 cm and 10 cm. Find each side of the rhombus.
Solution
We have,
ABCD is a rhombus with diagonals AC = 10 cm and BD = 24 cm
We know that diagonal of a rhombus bisect each other at 90°
∴ AO = OC = 5 cm and BO = OD = 12 cm
In ΔAOB, by Pythagoras theorem
AB2 = AO2 + BO2
⇒ AB2 = 52 + 122
⇒ AB2 = 25 + 144 = 169
⇒ AB = `sqrt169` = 13 cm
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