SOLUTION: As part of a landscaping​ project, put in a flower bed measuring 18 feet by 22 feet. Surround the bed with a uniform border of​ low-growing plants. a. Write a polynomial that

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: As part of a landscaping​ project, put in a flower bed measuring 18 feet by 22 feet. Surround the bed with a uniform border of​ low-growing plants. a. Write a polynomial that       Log On


   

Question 1134642: As part of a landscaping​ project, put in a flower bed measuring 18 feet by 22 feet. 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 flower bed.
b. The low growing plants surrounding the flower bed require 1 square foot each when mature. If there are 384 of these​ plants, how wide a strip around the flower bed should be prepared for the​ border?
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
u, the uniform width surrounding the flower bed
A, the area of the border surrounding the flower bed
%2818-2u%29%2822-2u%29-18%2A22=A

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If 1 plant needs 1 square foot, and if 384 of the low growing plants, then this means border containing the low grow plants must be 384 square feet.
%2818-2u%29%2822-2u%29=384%2B18%2A22
Simplify and solve.

2%2A2%2A%289-u%29%2811-u%29=780
2%2A2%2A%289-u%29%2811-u%29=4%2A195
%289-u%29%2811-u%29=195
.
.



Note that 195=13%2A15, and the two binomial factors on the left differ by two.