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A factory is to be built on a lot measuring 150 ft by 200 ft. A local building code specifies that a lawn of uniform width and equal in area to the factory must surround the factory.

Answer :

thaovtp1407

Answer:

21000

Step-by-step explanation:

Let x = the width of the lawn

Find the total area of the factory and the lawn: 200 * 210 = 42000 sq/ft

Factory area has to equal lawn area, therefore

21000 sq/ft = area of the lawn and the factory

The dimensions of the factory: (200-2x) by (210-2x)

Find x using the area of the factory

(200-2x) * ( 210-2x) = 21000

42000 - 420x - 400x + 4[tex]x^{2}[/tex] = 21000

<=> [tex]x^{2}[/tex] - 205x + 5250 = 0

<=> (x-30)(x-175) = 0

<=> x= 30 or x=175 but x = 30 ft is the solution that makes sense for the width of the lawn, so

  • Length: 210 - 2(30) = 150 ft
  • Width: 200 - 2(30) = 140 ft

Thus we have the area of the factory using these dimensions:

150 * 140 = 21000

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