Question

The base and corresponding altitude of a parallelogram are 10 cm and 12 cm respectively. If the other altitude is 8 cm, find the length of the other pair of parallel sides.

Answer 1

We have,
ABCD is a parallelogram with side AB = CD = 10 cm (Opposite sides of parallelogram are equal) and corresponding altitude AM = 12 cm.
The other side is AD and the corresponding altitude is CN = 8 cm


Area of a parallelogram = Base × Height
We have two altitudes and two corresponding bases.
So,2×BC×CF =12×AB×AE
⇒ AD x CN = CD x AM
⇒ AD x 8 = 10 x 12

⇒ AD = $\frac{10\times 12}{8}=15\mathrm{cm}$
Hence, the length of the other pair of the parallel side = 15 cm.