Final answer:
To find the length of each piece, we divide the total length of the rope by the sum of the ratios. The longest piece is 5/10 of the total length and the shortest piece is 2/10 of the total length. The longest piece is 9 inches longer than the shortest piece.
Step-by-step explanation:
To find the length of each piece of rope, we need to first find the total length of the rope. We can do this by converting the given length from feet and inches to inches only. 2 feet is equal to 24 inches, and 6 inches is an additional 6 inches. So the total length of the rope is 24 + 6 = 30 inches.
The ratio given is 2:3:5. To find the length of each piece, we can divide the total length (30 inches) by the sum of the ratios (2 + 3 + 5 = 10).
The longest piece is 5/10 of the total length, which is (5/10) * 30 = 15 inches.
The shortest piece is 2/10 of the total length, which is (2/10) * 30 = 6 inches.
The longest piece is 15 inches and the shortest piece is 6 inches, so the longest piece is 15 - 6 = 9 inches longer than the shortest piece.
If the pieces are cut in a 1:2:3 ratio, the total length of the rope is still 30 inches.
In this case, the longest piece is 3/6 of the total length, which is (3/6) * 30 = 15 inches.
The shortest piece is 1/6 of the total length, which is (1/6) * 30 = 5 inches.
The longest piece is 15 inches and the shortest piece is 5 inches, so the longest piece is 15 - 5 = 10 inches longer than the shortest piece.