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Let's assume the lengths of the legs are 'x' and 'x + 3'. Using the Pythagorean theorem, we have x² + (x + 3)² = h². For instance, when x = 4, then (x + 3) = 7. Thus, the hypotenuse, h = √(4² + 7²) = √65 ≈ 8.06 cm. Let’s try another example. When x = 5, then (x + 3) = 8. Thus, h = √(5² + 8²) = √89 ≈ 9.43 cm. When x = 6, then (x + 3) = 9. Thus, h = √(6² + 9²) = √117 ≈ 10.82 cm. The key is understanding that we're dealing with a geometric problem where the lengths must satisfy both the Pythagorean theorem and the given condition. We can solve this with some good algebraic skills and an understanding of the Pythagorean theorem. Keep in mind that we need to find values that give us whole numbers or simple radicals. Let's see some common right-angled triangles that fit our description.
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