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Question
The diagonals of a rhombus are 8 cm and 15 cm. Find its side.
Solution
Given, AC = 15 cm, BD = 8 cm
Since, the diagonals of a rhombus bisects each other at 90°, therefore in the ΔAOB, we have
AB2 = OA2 + OB2
⇒ AB2 = `(15/2)^2 + (8/2)^2`
⇒ AB2 = (7.5)2 + (4)2
⇒ AB2 = 56.25 + 16
⇒ AB2 = 72.25
⇒ AB = `sqrt(72.25)`
⇒ AB = 8.5 cm
Since, it is a rhombus, the length of each side is 8.5 cm.
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