Let's solve the problem step-by-step:
1. Determine the initial length of the rope:
Given the remaining length of the rope before any cut is made, we have:
[tex]\[
8x + 7 \text{ cm}
\][/tex]
2. Calculate the length of the rope that is cut:
The length of the rope cut for use is:
[tex]\[
2x + 4 \text{ cm}
\][/tex]
3. Compute the remaining length of the rope after the cut:
Subtract the cut length from the initial length to find the remaining length of the rope:
[tex]\[
\text{Remaining length after cut} = (8x + 7) - (2x + 4)
\][/tex]
Simplify the expression:
[tex]\[
\text{Remaining length after cut} = 8x + 7 - 2x - 4 = 6x + 3
\][/tex]
4. Form a triangle with the remaining rope:
When the remaining rope is used to form a triangle with three equal sides, each side of the triangle will be:
[tex]\[
\text{Length of each side} = \frac{\text{Remaining length after cut}}{3}
\][/tex]
Substitute the remaining length after the cut:
[tex]\[
\text{Length of each side} = \frac{6x + 3}{3}
\][/tex]
5. Simplify the length of each side:
[tex]\[
\text{Length of each side} = \frac{6x}{3} + \frac{3}{3} = 2x + 1 \text{ cm}
\][/tex]
So, the length of each side of the triangle formed is:
[tex]\[
2x + 1 \text{ cm}
\][/tex]
