Question 1066940: A rectangular field is 150 feet by 250 feet. You begin clearing the outside of the field, how wide of a border around the field must you mow to complete 1/2 the job?
Teacher says we can you use calculator to check answer for this can you please explain how and how to solve problem. Thanks.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A rectangular field is 150 feet by 250 feet.
You begin clearing the outside of the field,
how wide of a border around the field must you mow to complete 1/2 the job?
:
Find the total area of the field:
150 * 250 = 37,500 sq/ft
then the mowed area and the remaining area are:
37500/2 = 18,750 sq/ft
:
Let x = the width of the border clears around the field
(150-2x)*(250-2x) = 18750
FOIL
37500 - 300x - 500x + 4x^2 = 18750
Arrange as a quadratic equation
4x^2 - 800x + 37500 - 18750 = 0
4x^2 - 800x + 18750 = 0
Use the quadratic equation to find x. a=4; b=-800; c=18750
My two solutions
x = 27.113
x = 172.887
Only reasonable solution is x = 27.113 ft is the width of border
:
:
Check this on your calc, find the area of the remaining field which is half so equal to area of the mowed part:
(150-2(27.113))*(250-2(27.113)) =
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