Question

Chris wants to make an enclosed rectangular area for a mulch pile. She wants to make the enclosure in such a way as to use a corner of her back yard. She also wants it to be twice as long as it is wide. Since the yard is already fenced, she simply needs to construct two sides of the mulch pile enclosure. She has only 15 feet of material available. Find the dimensions of the enclosure that will produce the maximum area

Answer 1

You imposed two conditions on the problem
1. the length is twice the width, and
2. the sum of length and width is 15

so clearly 2x + x = 15
x = 5

So it no longer is a problem dealing with maximimums.
the enclosure is 5 by 10 for an area of 50

(the maximum area would have been obtained by having two equal sides of 7.5 feet for an area of 56.25 feet^2, clearly larger than the 50 from above. But your condition of length = twice the width would not have been followed)