Let 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.
We know that area of a parallelogram = base x height.
We have two altitudes and two corresponding bases.
By equating them we get,
½ x BC x CF = ½ x AB x AE
On simplifying, we get
BC x CF = AB x AE
BC x 24 = 54 x 16
BC = (54 × 16)/24
= 36 cm
Hence, the length of the shorter side BC = AD = 36 cm.
