# Word Problem

### Word Problem

Mary is trying to put in a rectangular garden that is 5 feet longer than twice its width. He wants to have a sidewalk along two of the garden’s sides that is 3 feet wide. If the area of the sidewalk will be 213 ft2 ,help Mary find the dimensions of her garden.
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### Re: Word Problem

He is named "Mary"? (Probably British!) In any case, let "x" be the width of the garden, in fet so that the length, "5 feet longer than twice its width", is 2x+ 5. "He wants to have a sidewalk along two of the garden’s sides that is 3 feet wide." Which two sides? The two lengths? The two widths? One length and one width?

If the sidewalk is along the two lengths then it is 2 times 2x+ 5 by 3 feet, area 6(2x+ 5)= 12x+ 30= 213 so 12x= 193 and x= 183/12= 15.25 feet. The garden is 15 feet 3 inches wide and 35 feet 6 inches long.

If the sidewalk is along the two widths then it is 2 times x by 3 feet, area 6x= 213 so x= 213/6=35.5 feet. The grarden is 35 feet 6 inches wide and 76 feet long.

If the sidewalk is along one length and one width (most likely) then it is x+ 2x+ 1- 3= 3x- 2 by 3 feet (the "- 3" allows for the overlap at the corner where the two sides meet) so 3(3x- 2)= 9x- 6= 213. 9x= 219 so x= 219/9= 24 feet 4 inches. The garden is 24 feet 4 inches wide and 53 feet 8 inches long.

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