## You are building a rectangular planter for your school garden. You want the area of the planter to be 90ft. You want the length of the plant

Question

You are building a rectangular planter for your school garden. You want the area of the planter to be 90ft. You want the length of the planter to be 3ft longer than twice it’s width. What should the dimensions of the bottom of the planter be?

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Math
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2021-09-11T05:17:05+00:00
2021-09-11T05:17:05+00:00 1 Answer
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## Answers ( )

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