SOLUTION: Anton Smith is planning an expansion of a square flower garden in a city park. If each side of the original garden is increased by 4 meters, the new total area of the gardn will be

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Question 131658: Anton Smith is planning an expansion of a square flower garden in a city park. If each side of the original garden is increased by 4 meters, the new total area of the gardn will be 100 square meters. Find the length of each side of the original garden.
Answer by solver91311(24713) About Me  (Show Source):
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If the original side length is x, then the new side length must be x + 4. The area of a square is the length of the side squared, so

%28x%2B4%29%5E2=100

x%5E2%2B8x%2B16=100

x%5E2%2B8x-84=0

-6+%2A+14+=+-84 and -6%2B14=8, so

%28x-6%29%28x%2B14%29=0

So x=6 or x=-14. Since we are looking for a measure of length, -14 doesn't make sense, so we can exclude this root as extraneous caused by squaring the variable. The original length of the side of the garden is then 6 meters.

Check the answer: 6%2B4=10, 10%5E2=100