Question

# Given below is a parallelogram. AC and BD are diagonals. If AO = x + y, OC = 5y, DO = 3x, OB = 12, then find x and y.

A
x = 2, y = 3
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B
x = 1, y = 4
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C
x = 3, y = 2
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D
x = 4, y = 1
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Solution

## The correct option is C x = 4, y = 1In the parallelogram ABCD, AC and BD are diagonals. Since the diagonals of the parallelogram bisect each other, AO = OC and BO = OD. AO = x + y, OC = 5y (Given) ∴ x + y = 5y -----------(i) DO = 3x, OB = 12 ∴ 3x = 12 -------------(ii) On solving (ii), we get, x = 123 = 4. ∴ x = 4. Using x = 4 in (i), we get, 4 + y = 5y On solving, we get, 4 = 5y - y = 4y ⇒ 4y = 4 ⇒ y = 44 = 1 ∴ x = 4 and y = 1.

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