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

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.

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.