1990 AHSME Problems/Problem 27
Problem
Which of these triples could be the lengths of the three altitudes of a triangle?
Solution
Let , , and be the side lengths of the triangle such that . We are given by the triangle inequality.
Let , , and be the altitudes to sides , , and respectively. We see that . By computing the areas using , , and as bases we get Solving for and , plugging back into the triangle inequality, and canceling from both sides leaves us with Further manipulation gives
Looking at the answer choices and letting be the smallest value each time, we see that is not true. Thus, the answer is .
See also
1990 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 26 |
Followed by Problem 28 | |
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