Question

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.

Answer 1

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