Problem 283

Integer sided triangles for which the area/perimeter ratio is integral

Consider the triangle with sides 6, 8 and 10. It can be seen that the perimeter and the area are both equal to 24. So the area/perimeter ratio is equal to 1.
Consider also the triangle with sides 13, 14 and 15. The perimeter equals 42 while the area is equal to 84. So for this triangle the area/perimeter ratio is equal to 2.

Find the sum of the perimeters of all integer sided triangles for which the area/perimeter ratios are equal to positive integers not exceeding 1000.

面积周长比为整数的整数边三角形

考虑三边长为6、8、10的三角形，可以看出它的边长和面积都是24，因此它的面积周长比等于1。
再考虑三边长为13、14、15的三角形，它的周长是42，而面积是84，因此它的面积周长比等于2。

找出所有面积周长比为不超过1000的整数的整数边三角形，并求出它们的周长之和。