2006 iTest Problems/Problem 29
Problem
The altitudes in triangle have lengths 10, 12, and 15. The area of can be expressed as , where and are relatively prime positive integers and is a positive integer not divisible by the square of any prime. Find .
Solution (credit to jeffisepic)
Let be the area of the triangle. That makes the three side lengths . Since we know the lengths of all three sides, we can use Heron's Formula to solve for . Since the area can not equal 0, . Thus, .
See Also
2006 iTest (Problems, Answer Key) | ||
Preceded by: Problem 28 |
Followed by: Problem 30 | |
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