Final answer:
The length of the shorter piece of the 21-ft board is 8.5 ft.
Step-by-step explanation:
The length of the shorter piece of the 21-ft board can be found by setting up an equation. Let's call the length of the longer piece x. According to the problem, the shorter piece is 4 feet shorter than the longer piece. So, the length of the shorter piece is x - 4.
Since the two pieces together make up the entire 21-ft board, we can set up the equation: x + (x - 4) = 21.
By solving the equation, we find that the longer piece is 12.5 ft and the shorter piece is 8.5 ft.