# Polynomial Story Problem

• Nov 23rd 2009, 04:25 PM
mjfaris
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.
• Nov 23rd 2009, 05:05 PM
Soroban
Hello, mjfaris!

Did you make a sketch?

Quote:

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?

• Nov 23rd 2009, 05:14 PM
mjfaris
Thank you so much!
• Sep 17th 2012, 04:51 PM
drcottonpuss
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!