1996 AHSME Problems/Problem 23
Problem
The sum of the lengths of the twelve edges of a rectangular box is , and the distance from one corner of the box to the farthest corner is . The total surface area of the box is
Solution
Let , and be the unique lengths of the edges of the box. Each box has edges of each length, so: The spacial diagonal (longest distance) is given by . Thus, we have , so .
Our target expression is the surface area of the box:
Since is a symmetric polynomial of degree , we try squaring the first equation to get:
Substituting in our long diagonal and surface area expressions, we get: , so , which is option .
See also
1996 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 22 |
Followed by Problem 24 | |
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