Question

The given figure shows a parallelogram $ABCD$ with area $324sq.cm$. $P$ is a point in $AB$ such that $AP:PB=1:2.$

Find:the ratio $OP:OD$.

• A. $1:3$
• B. $2:1$
• C. $1:4$
• D. $4:3$

Answer 1

Answer: (A)

$1:3$

Given,
Area of a parallelogram $\square ABCD=324$sq.cm.

$P$ is a point in $AB$ such that $AP:PB=1:2$.

Now,

$AP:PB=1:2$.

$\frac{AP}{PB}=\frac{1}{2}=k$

$\Rightarrow AP=k$

$\Rightarrow PB=2k$

Now, $AB=AP+PB$

$=k+2k$

$=3k$

$AB=DC$ ....(opposite sides of parallelogram)

$△OPA\sim △ODC$

$\therefore \frac{OP}{OD}=\frac{AP}{DC}$

$\therefore \frac{OP}{OD}=$$\frac{k}{3k}$

$\therefore \frac{OP}{OD}=$$\frac{1}{3}$