Question

$ABCD$ is parallelogram whose diagonals intersect at $O$. If $OD=9cm,OB=x+ycm,OA=x-y$, and $OC=5cm$, find $x$ and $y$.

Answer 1

Since diagonals of a parallelogram bisect each other.

$x+y=9$ -(i) and $x-y=5$ -(ii)

solving both we get

$2x=14\Rightarrow x=7$cm and $7-y=5$

$\to y=2$cm

$\therefore x=7$cm and $y=2$cm