Question

ABCD is a parallelogram DE is perpendicular to AB.
AB = 30 cm
DE = 15 cm
BC = 25 cm

Find the length of DF, where DF is perpendicular to BC.
.

Answer 1

The length of DF is 18 cm

Answer 2

The length of DF is 18 cm.

Step-by-step explanation:

Given:

ABCD is a parallelogram DE is perpendicular to AB.

AB = 30 cm

DE = 15 cm

BC = 25 cm

To Find:

DF = ?

Solution:

Area of Parallelogram is given by

$\textrm{Area of Parallelogram}=Base\times Height$

Area will remain same for same parallelogram with different Base-Height as shown in figure.

$\textrm{Area of Parallelogram ABCD}=\textrm{Area of Parallelogram ABCD}\\AB\times DE = BC\times DF$

Substituting the values we get

$30\times 15=25\times DF\\450=25\times DF\\\\\\DF=\frac{450}{25}=18\ cm\\ \therefore DF =18\ cm$

The length of DF is 18 cm.