The parallelogram area is 72 dm ^ 2. The distances from the point of intersection of its diagonals to the sides

The parallelogram area is 72 dm ^ 2. The distances from the point of intersection of its diagonals to the sides are 3 dm and 9 dm. Find the perimeter of the parallelogram.

Distances from the point of intersection of its diagonals to the sides are half the heights of the parallelogram
Hence, h1 = 3 * 2 = 6 dm h2 = 9 * 2 = 18 dm
The area of the parallelogram is equal to the product of the height by the side to which it is drawn: S = a * h1 S = b * h2a = S / h1 = 72/6 = 12 dm b = S / h1 = 72/18 = 4 dm
Perimeter is equal to twice the sum of adjacent sides P = 2 * (a + b) = 2 * (12 + 4) = 2 * 16 = 32 (dm)