Final answer:
To find the length of the longer segment of the diameter, use the Pythagorean theorem by setting up an equation with known lengths. Solve this equation to find the length of the longer segment.
Step-by-step explanation:
To find the length of the longer segment of the diameter, we can use the fact that the diameter is perpendicular to the chord. This means that the shorter segment of the diameter, the chord, and the longer segment of the diameter form a right triangle.
We can use the Pythagorean theorem to solve this triangle. The shorter segment of the diameter is 4 inches, and the length of the chord is 12 inches. Let's call the length of the longer segment of the diameter x.
By applying the Pythagorean theorem, we have 4^2 + x^2 = 12^2. Simplifying this equation, we get x^2 = 144 - 16, which gives us x^2 = 128. Taking the square root of both sides, we find that x is approximately 11.31 inches. Therefore, the length of the longer segment of the diameter is approximately 11.31 inches.