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Question

ABCD is a parallelogram. If AO = 10, OC = 3x + 4, BO = 8, OD = 2y + 2, then find the value of x and y.


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

The correct option is A x = 2, y = 3

ABCD is a parallelogram and, AC and BD are the diagonals.

We know that, the diagonals of a parallelogram bisect each other. ...(i)

Given, AO = 10, OC = 3x + 4, BO = 8, and OD = 2y + 2.

From (i),
AO = OC
10 = 3x + 4
3x = 10 - 4 = 6
3x = 6
x = 63 = 2.

From (i),
BO = OD
8 = 2y + 2
2y = 8 - 2 = 6
2y = 6
y = 62 = 3

Hence, x = 2, y = 3.

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