Question

Given below is a parallelogram. AC and BD are diagonals. If AO = x + y, OC = 5y, DO = 3x, OB = 12, they find x and y.

Answer 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)
x + y = 5y ------- (i)

DO = 3x, OB = 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