The two sides of an isosceles triangle are 6 cm and 12 cm. Find the perimeter of the triangle (in cm).

Options

A. 32
B. 30
C. 24
D. 18

Explanation

To find the perimeter of the isosceles triangle with two sides measuring 6 cm and 12 cm, we will follow these steps:

### Step 1: Identify the sides of the isosceles triangle
In an isosceles triangle, two sides are equal. Here, we have two given sides: 6 cm and 12 cm. Since the triangle is isosceles, we can assume that the two equal sides are the shorter ones, which are both 6 cm.

### Step 2: Determine the third side
Since we have assumed the two equal sides are 6 cm each, the third side must be 12 cm.

### Step 3: Check the triangle inequality theorem
Before calculating the perimeter, we need to ensure that the triangle can exist by checking the triangle inequality theorem. The sum of the lengths of any two sides must be greater than the length of the third side.

- Check: 6 cm + 6 cm > 12 cm
- Check: 6 cm + 12 cm > 6 cm
- Check: 12 cm + 6 cm > 6 cm

The first condition (6 + 6 > 12) does not hold true, which means that this configuration does not form a valid triangle.

### Step 4: Re-evaluate the sides
Since the configuration with two sides of 6 cm and one side of 12 cm does not satisfy the triangle inequality, we need to consider the possibility of having the two equal sides as 12 cm each, and the third side as 6 cm.

### Step 5: Calculate the perimeter
Now, if we have two sides of 12 cm and one side of 6 cm, we can calculate the perimeter:

Perimeter = Side1 + Side2 + Side3
Perimeter = 12 cm + 12 cm + 6 cm
Perimeter = 30 cm

### Final Answer
The perimeter of the triangle is **30 cm**.

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