The length of two sides of an isosceles triangle are 15 and 22 respectively. What are the possible values of perimeter ?

Options

A. 52 or 59
B. 52 or 60
C. 15 or 37
D. 37 or 29

Answer

To find the possible values of the perimeter of an isosceles triangle with two sides measuring 15 and 22, we can follow these steps:

### Step 1: Identify the sides of the isosceles triangle
In an isosceles triangle, two sides are equal. Therefore, we can have two scenarios:
1. The two equal sides are both 15.
2. The two equal sides are both 22.

### Step 2: Calculate the perimeter for each scenario

**Scenario 1: Two sides of length 15**
- The third side will be 22.
- The perimeter \( P \) is calculated as:
\[ P = 15 + 15 + 22 = 52 \]

**Scenario 2: Two sides of length 22**
- The third side will be 15.
- The perimeter \( P \) is calculated as:
\[ P = 22 + 22 + 15 = 59 \]

### Step 3: List the possible perimeters
From the calculations above, the possible values of the perimeter are:
- 52 (when the equal sides are 15)
- 59 (when the equal sides are 22)

### Conclusion
The possible values of the perimeter of the isosceles triangle are **52 and 59**.

---