SOLUTION: A rectangular garden has dimensions of 15 feet by 9 feet. A gravel path of equal width is to be built around the gard. How wide can the path be if there is enough gravel for 432

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Question 394643: A rectangular garden has dimensions of 15 feet by 9 feet. A gravel path of equal width is to be built around the gard. How wide can the path be if there is enough gravel for 432 ft^2?
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi

Let x represent the width of the walk. Garden has an Area= 15*9 = 135 ft^2

Question states***

 (15+2x)(9+2x) - 135ft^2 = 432ft^2, the area of the path.

solving for x

 135 + 48x + 4x^2 - 135 = 432

    4x^2 + 48x - 432 = 0

     x^2 + 12x - 108 = 0

factoring or using quadratic formula x+=+%28-12+%2B-+sqrt%28576+%29%29%2F%282%29+=+%28-12+%2B-+24%29%2F2+ 

   (x + 18)(x-6) = 0   |tossing out negative solution for length

            x = 6ft, the width of the walk