The height of the parallelogram is 6 cm more than the side to which it is drawn.

The height of the parallelogram is 6 cm more than the side to which it is drawn. How long can this height have if it is known that the area of the parallelogram is less than 160 cm2?

Let’s denote the side of the parallelogram by x, and the height drawn to it (x + 6). The parallelogram area is found by the formula:
S = a * h, where a is the side, h is the height drawn to it. By the condition of the problem, we know that the area is 160 cm², we can draw up an equation.
x * (x + 6) = 160
x² + 6x = 160
x² + 6x – 160 = 0
D = 6² – 4 * 1 * (-160) = 36 + 640 = 676
x1 = (-6 + √767) / 2 = (-6 + 26) / 2 = 10
x2 = (-6 – √767) / 2 = (-6 – 26) / 2 = -16
Only a positive root is suitable for us, which means that the side of the parallelogram is 10 cm, and the height is:
x + 6 = 10 + 6 = 16 cm.
Answer: height 16 cm.