Let's denote the length of the larger piece as \( x \) meters. According to the problem, the length of the smaller piece is 5 meters greater than that of the larger piece.
However, it is also given that the length of the smaller piece is actually 12 meters.
So we can set up the equation:
\[ \text{Smaller piece} = \text{Larger piece} + 5 \]
Substituting the known value:
\[ 12 = x + 5 \]
Now, we solve for \( x \):
\[ x = 12 - 5 \] \[ x = 7 \text{ meters} \]
So, the length of the larger piece is 7 meters.
Now we can find the total length of the carpet by adding the lengths of both pieces:
\[ \text{Total length} = \text{Smaller piece} + \text{Larger piece} = 12 + 7 \] \[ \text{Total length} = 19 \text{ meters} \]
In summary:
- The length of the larger piece is 7 meters.
- The total length of the carpet is 19 meters.
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