Question

select the correct answer from each drop-down menu. a machine cuts a strip of carpet into two pieces. the length of the smaller piece is 5 meters greater than \\(\frac{1}{4}\\) the length of the larger piece. if the length of the smaller piece is 12 meters, the length of the bigger piece is 28 meters and the total length of the carpet is meters. 25.5 26 32 40

Explanation:

Step1: Find the length of the larger piece (already given as 28, but let's verify)

Let \( L \) be the length of the larger piece. The smaller piece \( S = 12 \) meters, and \( S=\frac{1}{4}L + 5 \). Substituting \( S = 12 \):
\( 12=\frac{1}{4}L + 5 \)
Subtract 5: \( 12 - 5=\frac{1}{4}L \)
\( 7=\frac{1}{4}L \)
Multiply by 4: \( L = 28 \) (matches the given value).

Step2: Calculate total length

Total length = length of smaller piece + length of larger piece
Total = \( 12 + 28 = 40 \) meters.

Answer:

40