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Question
If length of both diagonals of rhombus are 60 and 80, then what is the length of side?
Options
100
50
200
400
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Solution
50
Explanation:
Let ABCD be the rhombus, diagonal AC = 60 and BD = 80.
We know that the diagonals of a rhombus are perpendicular bisectors of each other.
∴ Diagonals AC and BD bisect each other at point M.
∴ In ∆AMD, ∠M = 90°, AM = 30, DM = 40
∴ AM2 + DM2 = AD2 ...[Pythagoras theorem]
∴ (30)2 + (40)2 = AD2
∴ 900 + 1600 = AD2
∴ AD2 = 2500
∴ AD = 50 units
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