Behold a 13-14-15 triangle. The 15-long side is dissected into 5 equal parts and the 14-long side is dissected into 7 equal parts. What is the difference between the red and green areas?
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Red – green is 72/5.
First, one sees that red equals 4T/7-W, where T is the total area of the triangle and W is the sum of the white areas marked with x. Similarly, green equals 2T/5-W. Therefore red – green equals 6T/35. Now, T can be shown to be 84 using Heron’s formula. Therefore red – green = 72/5.