SOLUTION: You have a rectangular garden 15ft longer than it is wide. If a 4ft sidewalk goes around the garden and the area of the sidewalk is 632 squared feet, what is the length and width o

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Question 850245: You have a rectangular garden 15ft longer than it is wide. If a 4ft sidewalk goes around the garden and the area of the sidewalk is 632 squared feet, what is the length and width of the garden? (Use 1 variable)
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
Let w = width.
Length is w%2B15.
Garden area is w%28w%2B15%29.

The sidewalk forms an outer area and an inner area.
The outer area is %28w%2B2%2A4%29%28w%2B15%2B2%2A4%29=%28w%2B8%29%28w%2B23%29.

The sidewalk area is the outer area minus the inner(garden) area, and this area is given:
highlight_green%28%28w%2B8%29%28w%2B23%29-w%28w%2B15%29=632%29.
This is a quadratic equation just requiring some simplification and then finish with either factoring or general solution to a quadratic equation.
You take it from here.