1988 AHSME Problems/Problem 22
Problem
For how many integers does a triangle with side lengths and have all its angles acute?
Solution
We first notice that the sides and , can be part of different right triangles, one with sides , and the other with a leg somewhere between and . We now notice that if is less than or equal to , one of the angles is obtuse, and that the same is the same for any value of above . Thus the only integer values of that fit the conditions, are So, the answer is
See also
1988 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 21 |
Followed by Problem 23 | |
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