2008 AMC 8 Problems/Problem 17
Contents
[hide]Problem
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?
Solution
A rectangle's area is maximized when its length and width are equivalent, or the two side lengths are closest together in this case with integer lengths. This occurs with the sides . Likewise, the area is smallest when the side lengths have the greatest difference, which is . The difference in area is .
Video Solution
https://youtu.be/9bVwSsWa8IY Soo, DRMS, NM
See Also
2008 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 16 |
Followed by Problem 18 | |
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