To determine the original length given that [tex]\(6\%\)[/tex] of it is [tex]\(390\)[/tex] meters, we'll follow these steps:
1. Understand the relationship: We know that [tex]\(6\%\)[/tex] of the original length is equal to [tex]\(390\)[/tex] meters.
2. Express in mathematical terms: Let's denote the original length as [tex]\(L\)[/tex]. We know that [tex]\(6\%\)[/tex] of [tex]\(L\)[/tex] can be written mathematically as [tex]\(0.06L\)[/tex]. According to the problem, this equals [tex]\(390\)[/tex] meters.
[tex]\[
0.06L = 390
\][/tex]
3. Solve for [tex]\(L\)[/tex]: To find the original length [tex]\(L\)[/tex], we need to isolate [tex]\(L\)[/tex] on one side of the equation. We do this by dividing both sides of the equation by [tex]\(0.06\)[/tex]:
[tex]\[
L = \frac{390}{0.06}
\][/tex]
4. Perform the division: Carry out the division to determine the value of [tex]\(L\)[/tex]:
[tex]\[
L = 6500
\][/tex]
Therefore, the original length is [tex]\(6500\)[/tex] meters.
