SOLUTION: a factory measuring 80m by 60m is to be surrounded be a sidewalk uniform in width. if the area of the factory is doubled by extending all sides, what is the width of the sidewalk(r

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: a factory measuring 80m by 60m is to be surrounded be a sidewalk uniform in width. if the area of the factory is doubled by extending all sides, what is the width of the sidewalk(r      Log On


   

Question 131950: a factory measuring 80m by 60m is to be surrounded be a sidewalk uniform in width. if the area of the factory is doubled by extending all sides, what is the width of the sidewalk(round to the nearest tenth)?
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
If the width of the sidewalk is x, then the outside dimensions of the area covered by the factory AND the sidewalk must be 60+%2B+2x and 80+%2B+2x. See figure:



The area covered by the factory is 60%2A80=4800 square meters

The area covered by the factory AND the sidewalk is %2860%2B2x%29%2880%2B2x%29=2%2A4800=9600 square meters.

Expand and collect terms:
4800%2B120x%2B160x%2B4x%5E2=9600
4800%2B280x%2B4x%5E2=9600

Add -9600 to both sides and put in standard form:
4x%5E2%2B280x-4800=0

Divide through by 4:
x%5E2%2B70x-1200=0

Complete the square:
x%5E2%2B70x=1200
x%5E2%2B70x%2B35%5E2=1200%2B35%5E2=1200%2B1225=2425
%28x%2B35%29%5E2=2425
x=-35%2B-sqrt%282425%29, but 2425=25%2A97 so,

x=-35%2B5sqrt%2897%29 or x=-35-5sqrt%2897%29. Second root is negative, but we are trying to determine a length measure, so discard the second root as extraneous.

x=-35%2B5sqrt%2897%29, to the nearest tenth, is 14.2 meters. I'll let you verify the arithmetic.