1988 AHSME Problems/Problem 23
Problem
The six edges of a tetrahedron measure and units. If the length of edge is , then the length of edge is
Solution
By the triangle inequality in , we find that and must sum to greater than , so they must be (in some order) and , and , and , and , or and . We try and , and now by the triangle inequality in , we must use the remaining numbers , , and to get a sum greater than , so the only possibility is and . This works as we can put , , , , , so that and also satisfy the triangle inequality. Hence we have found a solution that works, and it can be verified that the other possibilities don't work, though as this is a multiple-choice competition, you probably wouldn't do that in order to save time. In any case, the answer is , which is .
See also
1988 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 22 |
Followed by Problem 24 | |
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