Diagonals of a Parallelogram

Q. In the figure given below AN and CP are perpendiculars to the diagonal BD of a parallelogram. Which of the following options is correct?

1. AN=CP
2. AN < CP
3. None of these
4. AN > CP

Q. Find out the perpendicular distance between the parallel sides of the parallelogram if the ratio of the height and the base of the parallelogram having area P square unit is 3 : 5 .

Q. $P$ is a point on side $BC$ of a parallelogram $ABCD$. If $DP$ produced meets $AB$ produced at point $L$, prove that:

i) $DP:PL=DC:BL$

Q.

Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals

Q. In the above figure, $ABCD$ is a parallelogram, $AE\perp DC$ and $CF\perp AD$. If $AB=16cm,AE=8cm$ and $CF=10cm$, Find $AD.$

1. $AD=14.8cm$
2. $AD=11.8cm$
3. $AD=13.8cm$
4. $AD=12.8cm$