You manage network 10.9.0.0 (class A block 10.0.0.0/8) with 73 existing subnets and plan to add 27 more next year (total 100). To simplify management, you want the maximum possible hosts per subnet while meeting the subnet count. Which subnet mask should you use?

Introduction / Context:
Subnet design within private class A space (10.0.0.0/8) often balances the number of required subnets against the desire to keep many hosts per subnet. Borrowing more bits increases subnet count but reduces host capacity; the goal here is to borrow the minimum bits that satisfy the need for 100 subnets.

Given Data / Assumptions:

• Base network: 10.0.0.0/8; given network ID is 10.9.0.0 within that block.
• Subnets required: 73 existing + 27 new = 100 total.
• Objective: maximize hosts per subnet while meeting 100 subnets.

Concept / Approach:
Let n be the number of borrowed bits. Subnet count = 2^n. Choose the smallest n such that 2^n ≥ 100. Hosts per subnet = 2^(host_bits) - 2. With a class A /8, host_bits initially = 24. We want minimal n for 100 subnets to keep host_bits as large as possible.

Step-by-Step Solution:

Verification / Alternative check:
Subnets increment by 2 in the second octet (since mask 255.254.0.0); this produces 128 subnets maximum—meeting the 100 requirement with room for growth while preserving maximal host counts for this choice of n.

Why Other Options Are Wrong:

• 255.224.0.0 (/11), 255.240.0.0 (/12), 255.248.0.0 (/13), 255.252.0.0 (/14): each yields fewer than 100 subnets (2^(3..6) = 8..64), thus insufficient.
• 255.254.0.0 (/15) is the first mask that meets ≥100 subnets, keeping hosts per subnet as large as possible.

Common Pitfalls:
Forgetting to choose the minimal n that satisfies the subnet requirement; confusing classless allocation with classful defaults yet the math for borrowed bits remains identical; overlooking that /16 would halve host capacity vs /15 without being necessary for 100 subnets.

Final Answer:
255.254.0.0