The lengths of the sides of a right-angled triangle are consecutive even integers (in cm). What is the product of these integers?

Explanation

Let the sides be x-2, x, and x+2. By the Pythagorean theorem, (x-2)^2 + x^2 = (x+2)^2. This simplifies to x^2 - 4x + 4 + x^2 = x^2 + 4x + 4 \Rightarrow x^2 - 8x = 0, giving x = 8. The sides are 6, 8, and 10. Their product is 6 \times 8 \times 10 = 480.

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