SOLUTION: A rectangular garden has dimensions of 15 feet by 11 feet. A gravel path of uniform width is to be built around the garden. How wide can the path be if there is enough gravel for

Question 194173: A rectangular garden has dimensions of 15 feet by 11 feet. A gravel path of uniform width is to be built around the garden. How wide can the path be if there is enough gravel for 192 square feet?
Answer by RAY100(1637) (Show Source): You can put this solution on YOUR website!
outside area minus inside area = 192
inside dim = ( 11*15 = 165)
,
outside dim = (11+2w)(15+2w) = 165 +22w +30w +4w^2=4w^2+52w+165
,
Area difference = 4w^2 +52w +165 -165 = 192
,
4w^2 +52w -192 = 0
,
4 ( w^2 +13 w -48 ) =0
,
w^2 +13w -48) =0
factor
( w +16)(w-3) =0
w=-16, (not realistic),,,,,and w = 3
,
checking
outside dim,,,17 x 21,,, a= 357
inside dim 11 x 15 ,,,a=165
difference of area = 192,,,ok
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