SOLUTION: A farmer has a 200 feet by 40 feet rectangular field that he wants to increase by 24.8% by cultivating a strip of uniform width around the current field. How wide of a strip should

Algebra ->  Rectangles -> SOLUTION: A farmer has a 200 feet by 40 feet rectangular field that he wants to increase by 24.8% by cultivating a strip of uniform width around the current field. How wide of a strip should      Log On


   

Question 1166190: A farmer has a 200 feet by 40 feet rectangular field that he wants to increase by 24.8% by cultivating a strip of uniform width around the current field. How wide of a strip should he cultivate around the edge of his field to do this?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A farmer has a 200 feet by 40 feet rectangular field that he wants to increase by 24.8% by cultivating a strip of uniform width around the current field.
How wide of a strip should he cultivate around the edge of his field to do this?
:
Find the area of the original field: 200 * 40 = 8000 sq/ft
Find the area of the new field: 1.248 * 8000 = 9984 sq/ft
:
let x = the width of the strip around the original field
:
(2x+200)*(2x+40) = 9984
FOIL
4x^2 + 80x + 400x + 8000 = 9984
Arrange as a quadratic equation
4x^2 + 480x + 8000 - 9984 = 0
4x^2 + 480x - 1984 = 0
simplify, divide by 4
x^2 + 120x - 496 = 0
Use the quadratic formula a=1; b=120, c=-496, but this will factor to
(x-4)(x+124) = 0
positive solution is what we want here
x = 4 ft is the width of the strip around the field
;
:
See if that works
208 * 48 = 9984