SOLUTION: A rectangular flower bed 30 yards long by 24 yards wide has a walk of uniform width around it. If the area of the path is 1/4 that of the flower bed, find the width of the path.
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Question 198566: A rectangular flower bed 30 yards long by 24 yards wide has a walk of uniform width around it. If the area of the path is 1/4 that of the flower bed, find the width of the path. Answer by solver91311(24713) (Show Source):
The rectangle described by the outer edge of the path has to be by . Furthermore, the entire area of the flower bed and path together has to be times the area of the flower bed by itself (one whole flower bed plus 1/4 of a flower bed):
So:
and:
Expand the binomial expressions, put the quadratic equation in standard form, and solve by ordinary methods. In this case, ordinary methods will require either completing the square or using the quadratic formula.
