SOLUTION: The lengths of the sides of a triangle are positive integers. One side has length 17cm and the perimeter of the triangle is 50cm. If the area is also an integer, then the length of

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Question 1114709: The lengths of the sides of a triangle are positive integers. One side has length 17cm and the perimeter of the triangle is 50cm. If the area is also an integer, then the length of the shortest side is divisible by
a)2 b)3 c)5 d)7 e)11
Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!


I haven't found a good purely algebraic way to solve the problem....

By trial and error, I found that, if the other two sides are 17 and 16, then the triangle is an isosceles triangle with base 16. The altitude divides the triangle into two congruent right triangles, each with one leg 8 and hypotenuse 17. That makes the altitude 15, resulting in an integer value for the area.

The shortest side is 16, which is divisible only by answer a, 2.

Answer: a) 2
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