Final answer:
Using the Pythagorean theorem, we determine that the shortest side 'a' measures 5 units, resulting in the other side measuring 9 units and the hypotenuse measuring 11 units.
Step-by-step explanation:
The problem stated is a classic example of an application of the Pythagorean theorem, which defines the relationship between the lengths of the sides of a right triangle. The student is given that the hypotenuse is one unit more than twice the length of the shortest side (let's call the shortest side 'a', then the hypotenuse is '2a + 1'). The other side is described as one unit less than twice the length of the shortest side (which would be '2a - 1').
To find the lengths of the sides, we set up the equation based on the Pythagorean theorem: a² + (2a - 1)² = (2a + 1)². Expanding and simplifying this, we get an equation in terms of 'a', which we can solve to find the length of the shortest side. Once 'a' is determined, the other lengths can be calculated directly using the given relationships.
Upon solving the equation, we find 'a' equals 5 units. Therefore, the length of the other side (2a - 1) equals 9 units, and the hypotenuse (2a + 1) equals 11 units, which correspond to the lengths of the two sides of the triangle other than the shortest.