Final answer:
The length of AB is 4 centimeters.
Step-by-step explanation:
In the given problem, points A, B, and C are midpoints of the sides of right triangle DEF. Triangle ABC is inside triangle DEF, where angle DFE and angle ABC are right angles. The length of DE is 10 centimeters, the length of FD is 6 centimeters, and the length of FE is 8 centimeters.
To find the length of AB, we can use the Midpoint Theorem. The Midpoint Theorem states that the segment joining the midpoints of two sides of a triangle is parallel to the third side and half its length.
Since A is the midpoint of FD and B is the midpoint of DE, AB is parallel to EF. Also, AB is equal to half the length of EF. Therefore, AB = 8/2 = 4 centimeters.