SOLUTION: A 2 ft. wide path is made around a square garden. The path is 376 sq. ft. in area. Determine a side of the garden. S = side Area of garden; S * S = S^2 Not sure how t

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: A 2 ft. wide path is made around a square garden. The path is 376 sq. ft. in area. Determine a side of the garden. S = side Area of garden; S * S = S^2 Not sure how t      Log On

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Question 1158846: A 2 ft. wide path is made around a square garden. The path is 376 sq. ft. in area. Determine a side of the garden.
S = side
Area of garden; S * S = S^2

Not sure how to proceed.

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The square garden is s feet on a side; its area is s^2.

With the path 2 feet wide around the garden, the garden plus path makes a square (s+4) feet on a side.

The area of the path (376 sq ft) is the area of the garden plus path, minus the area of the garden:

376+=+%28s%2B4%29%5E2+-+s%5E2
376+=+s%5E2%2B8s%2B16-s%5E2
376+=+8s%2B16
360+=+8s
s+=+45

You can come up with the same equation to solve using common sense instead of formal algebra.

With s the length of a side of the garden, the 2 foot wide path consists of a strip with area 2 times s on each of the four sides, plus a 2-by-2 square in each corner; the total area of the path is 376 sq ft:

4%282s%29%2B4%282%2A2%29+=+376
8s%2B16+=+376

Same equation as before....