Question

Two sides of a parallelogram are 20 cm and 25 cm. If the altitude corresponding to the sides of length 25 cm is 10 cm, find the altitude corresponding to the other pair of sides.

Answer 1

We have,
ABCD is a parallelogram with longer side AB = 25 cm and altitude AE = 10 cm.
As ABCD is a parallelogram .hence AB=CD (opposite sides of parallelogram are equal)
The shorter side is AD = 20 cm and the corresponding altitude is CF.


Area of a parallelogram = Base × Height
We have two altitudes and two corresponding bases.
So,2×BC×CF =12×AB×AE
⇒ AD x CF = CD x AE
⇒ 20 x CF = 25 x 10
∴ CF = $\frac{25\times 10}{20}=12.5\mathrm{cm}$54×1624=36 cm
Hence, the altitude corresponding to the other pair of the side AD is 12.5 cm.