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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 = 1
In 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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