Question

Given below is a parallelogram. AB and CD are diagonals. If AO = x + y, OB = 5y, DO = 3x, OC = 12, then find x and y.

Answer 1

In the parallelogram ABCD, AB and CD are diagonals.
Since the diagonals of the parallelogram bisect each other,
AO = OB and CO = OD.

AO = x + y, OB = 5y (Given)

x + y = 5y ..............(i)

DO = 3x, OC = 12

3x = 12 .............(ii)

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

x = 4.

Using x = 4 in (i), we get, 4 + y = 5y

On solving, we get, 4 = 5y - y = 4y

4y = 4

$y=\frac{4}{4}=1$

x = 4 and y = 1.