Difference between revisions of "1996 AHSME Problems/Problem 23"
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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 | |
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 • 26 • 27 • 28 • 29 • 30 | ||
All AHSME Problems and Solutions |
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