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

zi2lalZ

zi2lalZ

Answered question

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 504ft2, find the width (x) of the strip.

Answer & Explanation

Benedict

Benedict

Skilled2020-12-07Added 108 answers

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
4x2+130x+10001000=504
4x2+130x504=0
Solve the quadratic equation. First, divide both sides by 2:
2x2+65x252=0
Factor:
(x+36)(2x-7)=0
x=36,x=72=3.5
Width can't be negative, so the strip must be 3.5ft. wide.

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