Question 575401: What is the area of the smallest scalene triangle whose side lengths are prime numbers? please explain
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! A scalene triangle is a triangle whose sides' lengths are all different. Prime numbers are positive integers other than 1 that can only be divided by 1 and themselves. The smallest prime numbers are 2, 3, 5, 7, 11, 13, 17 and 19.
In a triangle, the lengths of the two shortest sides add to more than the length of the third side, and the difference in length between the two longest sides must be less than the length of the shortest side. That disqualifies 2 as a side length.
A triangle with sides measuring 3, 5, and 7 is the smallest triangle we can make to satisfy the requirements of the problem.
Replacing another larger prime number for 3, 5, or 7 would obviously make the triangle larger.
The area of a triangle can be calculated from the lengths of all 3 sides using Heron's formula.
For a triangle with sides of length a, b, and c, Heron's formula states that
For our smallest triangle, with a=3, b=5, and c=7, the area would be
 = approx. 6.495
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