1. **Stating the problem:** We are given a polygon with sides labeled $a$, $b$, and $c$, all greater than zero. We need to determine which of the given expressions is *not* equal to the perimeter of this polygon. 2. **Understanding the perimeter:** The perimeter of a polygon is the sum of the lengths of all its sides. Since the polygon is formed with sides $a$, $b$, and $c$, the perimeter $P$ is the sum of these sides counted according to the polygon's shape. 3. **Analyzing the polygon shape:** The polygon is an upside-down "L" shape with three sides labeled $a$, $b$, and $c$. The perimeter includes: - The top horizontal side of length $a$ - The vertical right side of length $b$ - The bottom horizontal side of length $c$ - The other sides that complete the polygon, which based on the shape, include multiples of these segments. 4. **Calculating the perimeter:** From the diagram, the polygon's perimeter is composed of: - Two segments of length $a$ (top and bottom horizontal parts) - Two segments of length $b$ (vertical parts) - Four segments of length $c$ (horizontal parts at the bottom) Thus, the perimeter is: $$P = 2a + 2b + 4c$$ 5. **Checking each expression:** - (A) $4a - 4b$ is not a sum of positive lengths and can be negative, so unlikely to be perimeter. - (B) $a - b - Tc$ is unclear because $T$ is undefined; also subtracting lengths is not typical for perimeter. - (C) $8c$ is only multiples of $c$, ignoring $a$ and $b$. - (D) $2a + 2b + 4c$ matches our perimeter calculation. - (E) $3a - 3b + 2c$ includes subtraction, which is not typical for perimeter. 6. **Conclusion:** The expression that is *not* equal to the perimeter is (B) because it contains an undefined variable $T$ and subtracts lengths, which is inconsistent with perimeter calculation. **Final answer:** (B) $a - b - Tc$ is not equal to the perimeter.