2008 AIME I Problems/Problem 15
Problem
A square piece of paper has sides of length 100. From each corner a wedge is cut in the following manner: at each corner, the two cuts for the wedge each start at a distance 
from the corner, and they meet on the diagonal at an angle of 
(see the figure below). The paper is then folded up along the lines joining the vertices of adjacent cuts. When the two edges of a cut meet, they are taped together. The result is a paper tray whose sides are not at right angles to the base. The height of the tray, that is, the perpendicular distance between the plane of the base and the plane formed by the upped edges, can be written in the form ![$\sqrt[n]{m}$](http://latex.artofproblemsolving.com/c/f/1/cf14ec08d1380e317bdbb9e0ebeaa4ed75f72c17.png)
, where 
and 
are positive integers, 
, and is not divisible by the th power of any prime. Find 
.
Solution
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See also
| 2008 AIME I (Problems • Answer Key • Resources) | ||
| Preceded by Problem 14 |
Followed by Last Question | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
