A VLAN (Virtual Local Area Network) is a logical grouping of devices that share the same broadcast domain, regardless of their physical location or connection. VLANs can improve network performance, security, and management by separating different types of traffic, such as data, voice, and video1.
A VoIP (Voice over Internet Protocol) phone is a device that uses the Internet to transmit voice calls, instead of the traditional phone lines. VoIP phones require a network connection, an IP address, and a gateway to communicate with other VoIP devices or phone systems2.
A DHCP (Dynamic Host Configuration Protocol) server is a device that automatically assigns IP addresses and other network configuration parameters to devices that request them. DHCP simplifies network administration and avoids IP conflicts3.
A switchport is a physical interface on a switch that connects to a network device, such as a VoIP phone, a computer, or another switch. A switchport can be configured to belong to a specific VLAN or to carry traffic from multiple VLANs4.
A gateway is a device that connects different networks and enables communication between them. A gateway can also perform protocol conversion, such as translating between VoIP and analog signals5.
A route is a path that a packet takes to reach its destination. A route consists of a destination network, a next-hop device, and a metric. A router is a device that forwards packets based on their destination IP addresses and the routing table.
In order to allow a newly installed VoIP phone to operate correctly, the network administrator needs to assign the phone's switchport to the correct VLAN. This will ensure that the phone can communicate with the DHCP server and obtain an IP address that belongs to the same network as the phone system. This will also isolate the voice traffic from the data traffic and improve the quality of service.
Statically assigning the phone's gateway address is not enough to allow the phone to operate correctly, as the phone still needs an IP address and a subnet mask to communicate with other devices on the network. Moreover, statically assigning network parameters can be tedious and prone to errors, especially for a large number of devices.
Configuring a route on the VoIP network router is not necessary to allow the phone to operate correctly, as the phone and the phone system are on the same network and do not need to cross any routers. Configuring a route would only be needed if the phone and the phone system were on different networks and needed to communicate through a router.
Implementing a VoIP gateway is not required to allow the phone to operate correctly, as the phone and the phone system are both VoIP devices and use the same protocol. Implementing a VoIP gateway would only be needed if the phone or the phone system needed to communicate with a non-VoIP device or system, such as a traditional phone line or a public switched telephone network (PSTN).
Reference:
1: VLAN
2: VoIP Phone
3: DHCP
4: Switchport
5: Gateway
6: [Route]
7: [VoIP VLAN Configuration]
8: [Static vs Dynamic IP Addressing]
9: [Routing Basics]
10: [VoIP Gateway]

The best answer is B. Public address on the perimeter router.
Port address translation (PAT) is a function that allows multiple users within a private network to make use of a minimal number of IP addresses. Its basic function is to share a single IP public address between multiple clients who need to use the Internet publicly. It is an extension of network address translation (NAT)1.
PAT works by creating dynamic NAT mapping, in which a global (public) IP address and a unique port number are selected. The router keeps a NAT table entry for every unique combination of the private IP address and port, with translation to the global address and a unique port number2.
Therefore, an organization would use PAT for having a public address on the perimeter router, which can be shared by many hosts on the private network using different port numbers. This can reduce the bandwidth consumption and cost of the organization's internet connection, as well as provide some security benefits by hiding the internal network structure3.
The other options are not correct because:
VLANs on the perimeter are not related to PAT, as they are used to segment the network into logical groups based on different criteria, such as function, security, or performance4.
Non-routable address on the perimeter router would not allow the organization to access the Internet or the cloud, as non-routable addresses are not valid on the public network and cannot be translated by PAT5.
Servers on the perimeter are not a reason to use PAT, as servers usually have static IP addresses and do not need to share a public address with other hosts. Servers on the perimeter may use NAT, but not PAT, to map their private IP addresses to a public IP address2.

See the solution configuration below in Explanation
Explanation:

The DHCP scope defines the range of IP addresses that the DHCP server can assign to the devices on the network.
In this scenario, the network technician installed 35 additional workstations, which increased the demand for IP addresses on the network.
If the DHCP scope is not large enough to accommodate the new workstations, some of them will not be able to obtain an IP address from the DHCP server and will not be able to access network resources.
This would also affect the original workstations that were offline when the new workstations were turned on, as they would have to renew their IP addresses from the DHCP server when they come online.
To solve this problem, the network technician should check the DHCP scope and either increase the range of IP addresses or create a new scope for the additional workstations.
Incorrect VLAN setting, improper NIC setting, and duplicate IP address are not the most likely causes of this issue, as they would affect individual workstations or specific segments of the network, not the entire network. Reference:
[CompTIA Network+ N10-008 Study Guide], Chapter 2: Network Devices and Technologies, Section 2.2: Configure and Support IPv4 and IPv6 Addressing, p. 67-68
[Professor Messer's CompTIA N10-008 Network+ Course Notes], Section 1.3: Network Services, p. 13 Network+ N10-008 Practice Test | CertBlaster, Question 1

255.255.252.0 is a subnet mask that allows for 1022 network-connected devices on the same subnet, which is the smallest subnet that can accommodate 412 devices. The subnet mask determines how many bits are used for the network portion and how many bits are used for the host portion of an IP address. A smaller subnet mask means more bits are used for the network portion and less bits are used for the host portion, which reduces the number of available hosts on the subnet. 255.255.0.0 allows for 65534 hosts on the same subnet, which is too large. 255.255.254.0 allows for 510 hosts on the same subnet, which is also too large. 255.255.255.0 allows for 254 hosts on the same subnet, which is too small.