Final answer:
The question involved finding the side length of a square inscribed in a right triangle. The correct approach uses additional geometry to set up a system of equations resulting from segments on the legs of the triangle equal to the side length of the square. Solving these equations reveals that the side length of the square is 2 inches.
Step-by-step explanation:
The student is seeking to find the length of the side of a square inscribed in a right triangle with legs measuring 6 inches and 8 inches. To determine this, one can use the Pythagorean theorem which relates the legs of a right triangle to its hypotenuse. However, in this scenario, the side of the square also acts as a 'leg' of two smaller right triangles within the original triangle. The length of the square, let's call it 's', plus the square's length (again 's') will equal the longer leg of the triangle (8 inches); similarly, 's' plus the length from the corner of the square to the right angle of the triangle (which is also 's') will equal the shorter leg (6 inches).
Therefore, we have two equations: 2s = 8 and 2s = 6. Since both cannot be true with the same value of 's', we realize that the premise of the question must be reconsidered. The actual process involves a bit more geometry, using the fact that the segments along the legs that are not part of the square must be equal respectively, leading to a system of equations to solve for the length of the side of the square. Let's denote these segments as 'x'; hence the equations are s + x = 6 and s + x = 8. Subtracting these equations from the original leg lengths gives us x = 6 - s and x = 8 - s. As these segments are equal, we can set them equal to each other, getting 6 - s = 8 - s, which simplifies to s = 2 inches.