Answer: height = 6 units
Base = 7 units
Step-by-step explanation:
The formula for determining the area of a parallelogram is expressed as
Area = BH
B = 2x + 1
H = x + 3
If area = 42 square units, then
(2x + 1)(x + 3) = 42
2x² + 6x + x + 3 = 42
2x² + 7x + 3 - 42 = 0
2x² + 7x - 39 = 0
2x² + 13x - 6x - 39 = 0
x(2x + 13) - 3(2x + 13) = 0
x - 3 = 0 or 2x + 13 = 0
x = 3 or x = - 13/2 = - 6.5
Since x cannot be negative, then x = 3
Therefore,
Base = 2x + 1 = 2 × 3 + 1 = 7 units
Height = x + 3 = 3 + 3 = 6 units