X, Y and Z are three equilateral triangles. The sum of the areas of X and Y is equal to the area of Z. If the side lengths of X and Y are 6 cm and 8 cm respectively, then what is the side length of Z?
The correct answer is 10 cm.
So, the side lengths (6, 8, 10) form a Pythagorean triple, which is consistent with the area relationship given. This means if you construct equilateral triangles on the sides of a right-angled triangle, the sum of the areas of the triangles on the two shorter sides (legs) equals the area of the triangle on the longest side (hypotenuse). This is a geometric interpretation similar to the Pythagorean theorem itself, but for equilateral triangles built on the sides.
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