Original bandwidth $=100 \mathrm{Mbps}$
Original minimum frame size $= 512 \text{bits}$
Segment length increased by $50 \%$
New data rate $=1 \mathrm{Gbps}=1000 \mathrm{Mbps}$
Propagation speed $=2 \times 10^8 \mathrm{~m} / \mathrm{s}$
$\text{Transmission time of minimum frame} \geq 2 \times \text{Propagation delay across network}$
$$
\begin{gathered}
\text { Min Frame Size }=2 \times \frac{\text { Segment Length }}{\text { Propagation Speed }} \times \text { Data Rate } \\\\
512=2 \times \frac{L}{2 \times 10^8} \times\left(100 \times 10^6\right) \\\\
512=2 \times \frac{L}{2 \times 10^8} \times 10^8 \\\\
512=2 \times L \times 0.5
\end{gathered}
$$
Increased by $50\%:$
$$
L_{\text {new }}=512 \times 1.5=768 \mathrm{~m}
$$
\begin{aligned}
\text { Min Frame Size }_{\text {new }} & =2 \times \frac{768}{2 \times 10^8} \times\left(1000 \times 10^6\right) \\\\
=2 & \times \frac{768}{2 \times 10^8} \times 10^9 \\\\
= & 2 \times 768 \times 5 \\\\
= & 7680 ~\mathrm{bits}
\end{aligned}
