2008 iTest Problems/Problem 62
Revision as of 19:43, 4 August 2018 by Rockmanex3 (talk | contribs) (Solution to Problem 62 -- surprisingly simple)
Problem
Find the number of values of such that the number of square units in the area of the isosceles triangle with sides , , and is a positive integer.
Solution
Let be the angle between the two sides with length . The area of the triangle is equal to .
Note that , so we know that . Since is not an integer, for every integer from to , there are two possible values of since can either be acute or obtuse. Each corresponds to exactly one value of so there are values of such that the area of the triangle is a positive integer.
See Also
2008 iTest (Problems) | ||
Preceded by: Problem 61 |
Followed by: Problem 63 | |
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