Question

Micheal came up with a design of a rectangular patio that is 25 ft by 40 ft., and that is surrounded by a terraced strip of uniform width planted with small trees and shrubs. If the

Analytic geometry
ANSWERED
asked 2020-12-06

Micheal came up with a design of a rectangular patio that is 25 ft by 40 ft., and that is surrounded by a terraced strip of uniform width planted with small trees and shrubs. If the A of this terraced strip is \(504 ft^2\), find the width (x) of the strip.

Expert Answers (1)

2020-12-07
The area needed will be equal to the area of the rectangular patio substracted from the area of the larger rectangular, so:
(2x+40)(2x+25)-(40)(25)=504
Simplify
\(\displaystyle{4}{x}^{{2}}+{130}{x}+{1000}-{1000}={504}\)
\(\displaystyle{4}{x}^{{2}}+{130}{x}-{504}={0}\)
Solve the quadratic equation. First, divide both sides by 2:
\(\displaystyle{2}{x}^{{2}}+{65}{x}-{252}={0}\)
Factor:
(x+36)(2x-7)=0
\(\displaystyle{x}=-{36},{x}=\frac{{7}}{{2}}={3.5}\)
Width can't be negative, so the strip must be 3.5ft. wide.
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