The governing formula is:
$$
T_{t x_{-} \min } \geq 2 \times T_p
$$
To find the maximum cable length, we use the equality condition:
$$
T_{t x_{-} \min }=2 \times T_p
$$
Minimum Frame Size ( $L_{\text {min }}$ ):
- 128 bytes $=128 \times 8=1024$ bits
Bandwidth (BW):
- $100 \mathrm{Mbps}=100 \times 10^6$ bits per second
$$
\begin{aligned}
& T_{t x \_\min }=\frac{L_{\min }}{B W}=\frac{1024 \mathrm{bits}}{100 \times 10^6 \mathrm{bps}}=10.24 \times 10^{-6} \text { seconds }=10.24 \mu s \\
& 2 \times T_p=T_{t x \_\min } \\
& 2 \times T_p=10.24 \mu s \\
& T_p=\frac{10.24 \mu s}{2}=5.12 \mu s=5.12 \times 10^{-6} \text { seconds }
\end{aligned}
$$
Length $=$ Propagation Speed $\times$ Propagation Time
Propagation Speed $\left(V_p\right): 2 \times 10^8 \mathrm{~m} / \mathrm{s}$
Propagation Time ( $T_p$ ): $5.12 \times 10^{-6} \mathrm{~s}$
Maximum Length $=\left(2 \times 10^8 \mathrm{~m} / \mathrm{s}\right) \times\left(5.12 \times 10^{-6} \mathrm{~s}\right)$
Maximum Length $=10.24 \times 10^2$ meters
Maximum Length = $1024$ meters
