1. ## Polynomial Story Problem

As part of a landscaping project, you put in a flower bed measuring 10 feet by 12 feet. You plan to surround the bed with a uniform border of low-growing plants.

Write a polynomial that describes the area of the uniform border that surrounds the bed. Explain what you did and why.

The low-growing plants surrounding the flower bed require 1 sq. foot each when mature. If you have 168 of these plants, how wide a strip around the bed should you prepare the border? Explain what you did and why.

If someone can help me set up the problem, I can figure out how to solve it.

2. Hello, mjfaris!

Did you make a sketch?

You put in a flower bed measuring 10 feet by 12 feet.
You plan to surround the bed with a uniform border of low-growing plants.

(a) Write a polynomial that describes the area of the uniform border that surrounds the bed.
Explain what you did and why.

(b) The plants in the border require 1 ft² each when mature.
If you have 168 of these plants, how wide should the border be?
Code:
      : x :    12    : x :
- * - - -  - - - - - *
x |                  |
- |   * - -  - - *   |
|   |    12    |   |
10 |   |10        |   | 2x+10
|   |          |   |
- |   * - - -  - *   |
x |                  |
- * - - - - - -  - - *
2x+12

The inner bed is 10-by-12 feet.
. . Its area is: .$\displaystyle 10\cdot12 \:=\:120$ ft².

The border is $\displaystyle x$ feet wide.

The length of the entire garden is: $\displaystyle 2x+12$ feet.
The width of the entire garden is: $\displaystyle 2x+10$ feet.
. . Its area is: .$\displaystyle (2x+12)(2x+10)$ ft².

$\displaystyle \text{(Area of border)} \;=\;\text{(Area of entire garden)} - \text{(Area of inner bed)}$

So, we have: .$\displaystyle A \;=\;(2x+12)(2x+10) - 120$

Can you finish it now?

3. Thank you so much!

4. ## Re: Polynomial Story Problem

I understand how you got A. But, for the life of me I can not figure out B. This is also a problem for my algebra homework. Please help me!