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 \Rightarrow \textbf{(B)}$$ (Error compiling LaTeX. Unknown error_msg)2 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 |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
All AMC 12 Problems and Solutions |
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