You are given the perimeter of an isosceles triangle = `A` cms and each of the two equal side are `B` cms longer than the ` 3^(rd)` side . Which of the following is the length of equal side ?

Options

A. `(A - B)/(3)`
B. `A + (B)/(3)`
C. ` (A + B)/( 3)`
D. `(A)/(3) + B `

Answer

To solve the problem step by step, we will denote the variables clearly and derive the length of the equal sides of the isosceles triangle.

### Step-by-Step Solution:

1. **Define the Variables**:
- Let the length of the third side (the base) of the isosceles triangle be \( x \) cm.
- Since each of the two equal sides is \( B \) cm longer than the third side, the length of each equal side will be \( x + B \) cm.

2. **Write the Perimeter Equation**:
- The perimeter \( P \) of the triangle is given as \( A \) cm.
- The perimeter can also be expressed as the sum of all sides:
\[ P = x + (x + B) + (x + B) \]
- Simplifying this, we get:
\[ P = x + x + B + x + B = 3x + 2B \]

3. **Set Up the Equation**:
- Since the perimeter is given as \( A \), we can set up the equation:
\[ 3x + 2B = A \]

4. **Solve for \( x \)**:
- Rearranging the equation to isolate \( x \):
\[ 3x = A - 2B \]
- Dividing both sides by 3 gives:
\[ x = \frac{A - 2B}{3} \]

5. **Find the Length of the Equal Side**:
- The length of each equal side is \( x + B \):
\[ \text{Equal side} = x + B = \frac{A - 2B}{3} + B \]
- To combine the terms, we convert \( B \) into a fraction with a common denominator:
\[ \text{Equal side} = \frac{A - 2B}{3} + \frac{3B}{3} = \frac{A - 2B + 3B}{3} = \frac{A + B}{3} \]

6. **Final Result**:
- Therefore, the length of each equal side of the isosceles triangle is:
\[ \frac{A + B}{3} \text{ cm} \]