2008 AMC 8 Problem 17
Attempt Problem 17 of the 2008 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 2008 AMC 8 solutions, or check the answer key.
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17.
Ms. Osborne asks each student in her class to draw a rectangle with integer side lengths and a perimeter of units. All of her students calculate the area of the rectangle they draw. What is the difference between the largest and smallest possible areas of the rectangles?
Answer: D
Small hint:
A perimeter of means the side lengths have sum
Big hint:
For a fixed positive integer sum, the largest product uses numbers as close as possible.
Solution:
If the side lengths are and , then , so .
The smallest possible area comes from side lengths and , giving area .
The largest possible area comes from the closest integer pair with sum , namely and , giving area .
The difference is .
Thus, D is the correct answer.
Problem 17 in other years
- 1985 AMC 8
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