Question

(c) ABCD is a parallelogram with adjacent sides 24 cm and 32 cm. If its area is 384 sq cm, find the
distance between both the pairs of opposites sides.​

Answer 1

Answer:

16 sq.cm

Step-by-step explanation:

The length of side 24cm

Its corresponding height is 12cm

The area of parallelogram is 24×12=288cm

2

The length of another side is 18cm

The area of parallelogram is 288cm

2

Its corresponding height is

18

288

=16cm

Answer 2

The distance between the parallel lines of length 24cm and 32cm in the parallelogram is 16cm and 12cm respectively.

Given :

Length of one pair of sides of parallelogram( AB, CD) = 24cm

Length of other pair of sides of parallelogram(AD,BC) = 32cm

Area of parallelogram = 384 sq. cm

To Find :

Distance between both the pairs of parallel lines of the parallelogram

Solution :

The formula for the area of parallelogram as applied here is :

                $Area = b * h$

where b = base length i.e. length of one of the pair of parallel lines

           h = height i.e. distance between that pair of parallel lines

Finding the distance between parallel lines of 24cm :

Here, the base of the parallelogram is AB or CD i.e. 24 cm

                      $Area = b * h$

                      $384 = 24 * h$

                          $h_{24} = 384 / 24$

                          $h_{24} = 16 cm$

Finding the distance between parallel lines of 32cm :

Here, the base of the parallelogram is AD or CB i.e. 32 cm

                      $Area = b * h$

                      $384 = 32 * h$

                          $h_{32} = 384 / 32$

                          $h_{32} = 12 cm$

Hence, the distance between the parallel lines of length 24 cm is 16cm. And the distance between the parallel lines of length 32cm is 12cm.

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