Question

The adjacent sides of a parallelogram are 15 cm and 8 cm. If the distance between the longer sides is 4 cm, find the distance between the shorter sides.

Answer 1

ABCD is a parallelogram with side AB of length 15 cm and the corresponding altitude AE of length 4 cm.
The adjacent side AD is of length 8 cm and the corresponding altitude is CF.

Area of a parallelogram = Base × Height
We have two altitudes and two corresponding bases.
∴ AD × CF = AB × AE
⇒ 8 cm × CF = 15 cm ×4 cm
⇒ CF =$15\times \frac{4}{8}cm$ =$\frac{15}{2}cm$ = 7.5 cm
Hence, the distance between the shorter sides is 7.5 cm.