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

Answer 1

The correct option is D 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)
$\therefore$ x + y = 5y -----------(i)

DO = 3x, OB = 12
$\therefore$ 3x = 12 -------------(ii)

On solving (ii), we get, x = $\frac{12}{3}$ = 4.
$\therefore$ x = 4.

Using x = 4 in (i), we get, 4 + y = 5y
On solving, we get, 4 = 5y - y = 4y
$\Rightarrow$ 4y = 4
$\Rightarrow$ y = $\frac{4}{4}$ = 1

$\therefore$ x = 4 and y = 1.