In parallelogram ABCD, AO = (3x + 9) cm, OB = (5y – 5) cm, OC = (5x + 3), and DO = (2y + 7) cm. What are the values of y and x respectively.

3 and 4

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4 and 3

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6 and 4

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4 and 6

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Solution

The correct option is B 4 and 3
As in a paralleogram, diagonals bisect each other, we can write
AO = OC and DO = OB.
Hence, (3x+9) = (5x + 3)
5x - 3x = 9 - 3
2x = 6
x = 3.

Considering DO = OB , 2y + 7 = 5y - 5
5y - 2y = 7 - (-5)
3y = 7 + 5 = 12
y = 4.
Therefore, the values of y and x are 4 and 3 respectively.

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In parallelogram ABCD, AO = (3x + 9) cm, OB = (5y – 5) cm, OC = (5x + 3), and DO = (2y + 7) cm. What are the values of y and x respectively.​ ​

In parallelogram ABCD, AO = (3x + 9) cm, OB = (5y – 5) cm, OC = (5x + 3), and DO = (2y + 7) cm. What are the values of y and x respectively.