Answer: length = 15 ft
Width = 6 ft
Step-by-step explanation:
Let L represent the length of the rectangular planter.
Let W represent the width of the rectangular planter.
You want the area of the planter to be 90ft. It means that
LW = 90- - - - - - - - - -1
You want the length of the planter to be 3ft longer than twice its width. It means that
L = 2W + 3
Substituting L = 2W + 3 into equation 1, it becomes
W(2W + 3) = 90
2W² + 3W = 90
2W² + 3W - 90 = 0
2W² + 15W - 12W - 90 = 0
W(2W + 15) - 6(2W + 15) = 0
W - 6 = 0 or 2W + 15 = 0
W = 6 or W = - 15/2
Since the width cannot be negative, then W = 6
L = 2W + 3 = 2 × 6 + 3
L = 12 + 3
L = 15
