The perimeter of a triangle is 30cm. Two sides are 12cm and 10cm. What is the length of the third side of the triangle?

Answer

To find the length of the third side of the triangle, we can follow these steps:

### Step 1: Understand the formula for the perimeter of a triangle.
The perimeter of a triangle is the sum of the lengths of all three sides. If we denote the sides as \( a \), \( b \), and \( c \), then the formula is:
\[ \text{Perimeter} = a + b + c \]

### Step 2: Identify the given values.
From the question, we know:
- The perimeter of the triangle is \( 30 \) cm.
- Two sides of the triangle are \( 12 \) cm and \( 10 \) cm.

We can assign:
- \( a = 12 \) cm
- \( b = 10 \) cm

### Step 3: Set up the equation using the perimeter.
Using the perimeter formula, we can write:
\[ a + b + c = 30 \]
Substituting the values of \( a \) and \( b \):
\[ 12 + 10 + c = 30 \]

### Step 4: Simplify the equation.
Now, we can simplify the left side:
\[ 22 + c = 30 \]

### Step 5: Solve for the third side \( c \).
To find \( c \), we can subtract \( 22 \) from both sides:
\[ c = 30 - 22 \]
\[ c = 8 \]

### Conclusion:
The length of the third side of the triangle is \( 8 \) cm.

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