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 [$\because AO=OC$]
$\Rightarrow$ 2$y$ + 2 = 10 cm
$\Rightarrow$ 2$y$ = 10 - 2
$\Rightarrow$ 2$y$ = 8
$\Rightarrow$ $y$ = 4 cm
(1 mark)

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