Final answer:
The two lengths of the board after it is cut are 36 inches and 50 inches.
Step-by-step explanation:
To find the lengths of the two pieces, we can set up an equation based on the given information. Let x be the length of the first piece. The other piece is 14 inches longer, so its length would be (x + 14) inches. The total length of the board is 88 inches, so we have the equation: x + (x + 14) = 88. Solving this equation, we find that x = 36. Therefore, the lengths of the two pieces are 36 inches and 36 + 14 = 50 inches.