SOLUTION: 10) 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

Question 701552: 10) 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 factory that measures 120 m by 80 m?

Answer by josgarithmetic(39616) (Show Source): You can put this solution on YOUR website!
Removed earlier solution because was wrong, rechecked twice more, different but still wrong.
Two rectangles. Inner and outer. Inner is just factory area. Outer is the area of lawn and factory combined. Let x be distance from inner side to corresponding outer side, away from the corners locations. Know that the lawn includes four squares of x^2 area. Draw this picture.

Outer area rectangle = (120+2x)(80+2x)
The outer area is TWO times the inner area,
Outer area (120+2x)(80+2x)=2(120)(80)
2*2*(60+x)(40+x)=2*2*60*80
(60+x)(40+x)=4800
.
.

Use general solution to quadratic equation,

x= 20 the width. (the -140 number in expression is not sensible)
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