SOLUTION: a local building code requires that all factories must be surrounded by a lawn. the width of the lawn must be uniform and the area of the lawn must be equal to the area of the fact

Algebra ->  Rectangles -> SOLUTION: a local building code requires that all factories must be surrounded by a lawn. the width of the lawn must be uniform and the area of the lawn must be equal to the area of the fact      Log On


   

Question 994251: a local building code requires that all factories must be surrounded by a lawn. the width of the lawn must be uniform and the area of the lawn must be equal to the area of the factory. what must be the width of a lawn surrounding a rectangular that measures 120m by 80m?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
system%28u=unknownWidth%2CL=120%2Cw=80%29

Factory area, wL
Combined Factory & Lawn area, (w+2u)(L+2u)
Lawn area requirement, highlight_green%28%28L%2B2u%29%28w%2B2u%29-wL=wL%29

Simplify that equation and solve for u.

wL%2B2wu%2B2Lu%2B4u%5E2-wL=wL
%282w%2B2L%29u%2B4u%5E2=wL
highlight_green%284u%5E2%2B%282w%2B2L%29u-wL=0%29

Substitute whenever you are ready, but solve for u. Formula for general solution of quadratic equation can be used.

u=%28-%282w%2B2L%29%2Bsqrt%28%282w%2B2L%29%5E2-4%2A4%2A%28-wL%29%29%29%2F%282%2A4%29
u=%28-2w-2L%2Bsqrt%284w%5E2%2B8wL%2B4L%5E2%2B4%2A4%2AwL%29%29%2F%282%2A4%29
u=%28-2w-2L%2B2%2Asqrt%28w%5E2%2B4wL%2BL%5E2%2B4wL%29%29%2F%282%2A4%29
highlight%28u=%28-w-L%2Bsqrt%28w%5E2%2B8wL%2BL%5E2%29%29%2F4%29


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The PLUS form is needed in the formula for quadratic equation because we must have a positive value for u. w and L are both positive, but they are used as SUBTRACTED in the numerator of the formula of quadratic equation solution.

Most of the time, students would want to substitute the given values just after finding the quadratic equation in the green rectangular outline shown (IF they are starting the problem solution and analysis in symbolic form as done in this example).

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

a local building code requires that all factories must be surrounded by a lawn. the width of the lawn must be uniform and the area of the lawn must be equal to the area of the factory. what must be the width of a lawn surrounding a rectangular that measures 120m by 80m?
Width of lawn: highlight_green%2820%29 m