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?