Question

The longer side of a parallelogram is 54 cm and the corresponding altitude is 16 cm. If the altitude corresponding to the shorter side is 24 cm, find the length of the shorter side.

Answer 1

We have,
ABCD is a parallelogram with the longer side AB = 54 cm and corresponding altitude AE = 16 cm.
The shorter side is BC and the corresponding altitude is CF = 24 cm.

Area of a parallelogram = base × height.We have two altitudes and two corresponding bases. So,
$\frac{1}{2}\times BC\times CF=\frac{1}{2}\times AB\times AE$
⇒ BC x CF = AB x AE
⇒ BC x 24 = 54 x 16
⇒ BC = $\frac{54\times 16}{24}=36\mathrm{cm}$
Hence, the length of the shorter side BC = AD = 36 cm.