Question

Given below is a parallelogram ABCD. Find the value of x and y.

(3 marks)

Answer 1

The given figure ABCD, is a parallelogram such that AO = 10 cm and BO = 12 cm.

For a parallelogram, we know that the diagonals bisects each other.

Hence, AO = OC and BO = OD

(1 mark)

Now,
OC = 10 cm [$\because AO=OC$]
$\Rightarrow$ 2y + 2 = 10 cm
$\Rightarrow$ 2y = 10 cm - 2 cm
$\Rightarrow$ 2y = 8 cm
$\Rightarrow$ y = 4 cm

(1 mark)

And,
OD = 12 cm [$\because OD=BO$]
$\Rightarrow$ 4x + 4 = 12 cm
$\Rightarrow$ 4x = 12 - 4 cm
$\Rightarrow$ 4x = 8 cm
$\Rightarrow$ x = 2 cm

(1 mark)