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
• B. x = 3, y = 2
• C. x = 1, y = 4
• D. x = 4, y = 1

Answer 1

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),
$\Rightarrow$ AO = OC
$\Rightarrow$ 10 = 3x + 4
$\Rightarrow$ 3x = 10 - 4 = 6
$\Rightarrow$ 3x = 6
$\Rightarrow$ x = $\frac{6}{3}$ = 2.

From (i),
$\Rightarrow$ BO = OD
$\Rightarrow$ 8 = 2y + 2
$\Rightarrow$ 2y = 8 - 2 = 6
$\Rightarrow$ 2y = 6
$\Rightarrow$ y = $\frac{6}{2}$ = 3

Hence, x = 2, y = 3.