2008 AMC 12B Problems/Problem 16
Problem
A rectangular floor measures by feet, where and are positive integers with . An artist paints a rectangle on the floor with the sides of the rectangle parallel to the sides of the floor. The unpainted part of the floor forms a border of width foot around the painted rectangle and occupies half of the area of the entire floor. How many possibilities are there for the ordered pair ?
Solution
By Simon's Favorite Factoring Trick:
Since and are the only positive factorings of .
or yielding solutions. Notice that because , the reversed pairs are invalid.
See Also
2008 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 15 |
Followed by Problem 17 |
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