Question

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?

Answer 1

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.