Question

The adjacent sides of a parallelogram are 36 cm and 27 cm in length. If the distance between the shorter sides is 12 cm, find the distanceе between the longer sides.

Answer 1

Given: The adjacent sides of a parallelogram are 36 cm and 27 cm. The distance between the shorter sides (corresponding altitude to side 27 cm) is 12 cm. (Area = base × corresponding height for a parallelogram.)

Step-wise calculation:

1. Let the distance between the longer sides (corresponding altitude to side 36 cm) be x cm.

2. Area = (Shorter side) × (Distance between the shorter sides)

= 27 × 12

= 324 cm²

3. Area = (Longer side) × (Distance between the longer sides)

= 36 × x

4. Equate areas: 36x = 324

⇒ `x = 324/36` 

= 9 cm

Or

`x = (27 xx 12)/36` 

= `3/4 xx 12` 

= 9

The distance between the longer sides is 9 cm.