`{:("Quantity A","Quantity B"),("The perimeter of Triangle ABC",22),("an isosceles triangle whose",),("longest side is equal to 11",):}`

Options

A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the infromation given.

Answer

To solve the problem, we need to analyze the given information about triangle ABC, which is an isosceles triangle with the longest side equal to 11. We will determine the perimeter of this triangle and compare it with the given quantity B, which is 22.

### Step-by-Step Solution:

1. **Identify the sides of the triangle**:
In an isosceles triangle, two sides are equal. Let's denote the lengths of the two equal sides as \( a \). Therefore, the sides of triangle ABC are \( a, a, \) and \( 11 \).

2. **Calculate the perimeter**:
The perimeter \( P \) of triangle ABC can be calculated as:
\[ P = a + a + 11 = 2a + 11 \]

3. **Apply the triangle inequality**:
For any triangle, the sum of the lengths of any two sides must be greater than the length of the third side. Since 11 is the longest side, we apply the triangle inequality:
\[ a + a > 11 \]
This simplifies to:
\[ 2a > 11 \]

4. **Solve for \( a \)**:
Dividing both sides of the inequality by 2 gives:
\[ a > 5.5 \]

5. **Substitute \( a \) back into the perimeter formula**:
Since \( a > 5.5 \), we can substitute this into the perimeter equation:
\[ P = 2a + 11 \]
If \( a \) is greater than 5.5, then:
\[ P = 2(5.5) + 11 = 11 + 11 = 22 \]
However, since \( a \) can be any value greater than 5.5, the minimum value of \( P \) is 22, but it can be greater than 22 depending on the value of \( a \).

6. **Conclusion**:
Since the perimeter \( P \) can be greater than 22, we conclude that:
\[ P > 22 \]
Therefore, Quantity A (the perimeter of triangle ABC) is greater than Quantity B (22).

### Final Answer:
Quantity A is greater than Quantity B.