SOLUTION: Julie stone designed a rectangular patio that is 25 ft by 40 ft. This patio is surrounded by a terraced strip of uniform width planted with small trees and shrubs. if the area A of

Question 101927: Julie stone designed a rectangular patio that is 25 ft by 40 ft. This patio is surrounded by a terraced strip of uniform width planted with small trees and shrubs. if the area A of this terraced strip is 504 ft^2, find the width of x of the strip.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
The essence of the problem:
:
a rectangle that is 25 ft by 40 ft. Surrounded by a strip of uniform width. if the area of this strip is 504 ft^2, find the width of x of the strip.
:
Given that: x = width of the strip
:
Overall area:
(2x+40)*(2x+25) = 4x^2 + 130x + 1000: FOILed
:
Rectangle area:
40 * 25 = 1000
:
Overall area - rectangle area = strip area
(4x^2 + 130x + 1000) - 1000 = 504
:
4x^2 + 130x + 1000 - 1000 - 504 = 0
:
4x^2 + 130x - 504 = 0; a quadratic equation
:
Simplify, divide by 2:
2x^2 + 65x - 252 = 0
:
Use the quadratic formula to find x: a=2; b=65; c=-252

Solution 1:

x = -36; obviously this is NOT the solution
Solution 2:

x = 3.5 ft is the width of the strip
:
:
Check our solution: 2x = 2(3.5) = 7
Overall area: 47 * 32 = 1504
Rectanglarea: 40 * 25 = 1000
-----------------------------
Difference area ******504 as given

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