Question

$ABCD$ is a parallelogram of area $162sq.cm$. $P$ is a point on $AB$ such that $AP:PB=1:2$.
Calculate the ratio $PA:DC$.

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

Answer 1

The correct option is A $1:3$

Given,

$ABCD$ is a parallelogram, Area of parallelogram $ABCD=162c{m}^2$

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

Now, $\frac{AP}{PB}=\frac{1}{2}=k$[Let]

Thus, $AP=k$ and $PB=2k$

And, $AB=AP+PB$

$=>AB=k+2k$

$=>AB=3k$

$\therefore \frac{AP}{AB}=\frac{1}{3}$

Now, $AB=CD$ [Opposite sides of a parallelogram are equal]

$\therefore \frac{AP}{CD}=\frac{1}{3}$