1999 AMC 8 Problem 5
Attempt Problem 5 of the 1999 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1999 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
5.
A rectangular garden feet long and feet wide is enclosed by a fence. To make the garden larger, while using the same fence, its shape is changed to a square. By how many square feet does this enlarge the garden?
Small hint:
Keep the perimeter the same
Big hint:
The square side length is one-fourth of the old perimeter
Solution:
The current length of the fence is feet. If all the sides become the same, then each side length is feet. As such, the area of the square is then square feet. Note that the original area of the garden is square feet.
Therefore, the difference is square feet.
Thus, D is the correct answer.
Problem 5 in other years
- 1985 AMC 8
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