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jor66
25.02.2020 •
Mathematics
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.
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Ответ:
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
= 21000
<=>
- 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 ftThus we have the area of the factory using these dimensions:
150 * 140 = 21000
Ответ: