One of the sides of a parallelogram is 4.2 cm and the altitude to that side is 3.6 cm. Find the perimeter of the parallelogram if the altitude to the other side is 2.4 cm.

The product of side length and altitude is area. The area remains the same regardless of how you measure it.

From the first side and altitude,

... area = side*altitude = (4.2 cm) * (3.6 cm) = 15.12 cm^2

From the second side and altitude

... area = side*altitude

... 15.12 cm^2 = side * (2.4 cm)

... side = (15.12 cm^2) / (2.4 cm) = 6.3 cm

The perimeter is the sum of the measures of all sides. Opposite sides are of equal measure.

... perimeter = 2 * (4.2 cm + 6.3 cm) = 21.0 cm