Dawn is trying to find the dimensions of a parallelogram. She knows that the base is one unit less than twice the height of the shape. The area is 91 square units. How long are the base and height?

Area of the parallelogram:

A = a * h

where a is the base and h is the height;

91 = a * h

a = 2 h + 1

(2 h + 1) * h = 91

2 h² + h - 91 = 0

h 1/2 = ( - 1 + / - √ (1+728)) / 4 = ( - 1 + / - 27) / 4

h = 6.5 (another solution is negative)

a = 2 * 6.5 + 1 = 13 + 1 = 14

Answer:

The base is 14 units and the height 6.5 units long.