The length of the base of an isosceles triangle is `2x - 2y + 4z`, and its perimeter is `4x + 6z`. Then the length of each of the equal sides is

Options

A. a)`x + y`
B. b)`x + y + z`
C. c)`2(x+y)`
D. d)`x + z`

Answer

To find the length of each of the equal sides of the isosceles triangle, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the components of the triangle**:
- Let the length of the base (B) be given as \( B = 2x - 2y + 4z \).
- The perimeter (P) of the triangle is given as \( P = 4x + 6z \).

2. **Set up the equation for the perimeter**:
- In an isosceles triangle, the perimeter is the sum of the lengths of the two equal sides (let's denote them as A) and the base. Therefore, we can express the perimeter as:
\[ P = A + A + B = 2A + B \]

3. **Substitute the known values into the perimeter equation**:
- We can substitute the values of P and B into the equation:
\[ 4x + 6z = 2A + (2x - 2y + 4z) \]

4. **Rearrange the equation to isolate 2A**:
- Rearranging gives:
\[ 2A = (4x + 6z) - (2x - 2y + 4z) \]

5. **Simplify the right-hand side**:
- Simplifying the right-hand side:
\[ 2A = 4x + 6z - 2x + 2y - 4z \]
\[ 2A = (4x - 2x) + (6z - 4z) + 2y \]
\[ 2A = 2x + 2y + 2z \]

6. **Divide by 2 to find A**:
- Now, divide both sides by 2:
\[ A = x + y + z \]

### Final Answer:
The length of each of the equal sides is \( A = x + y + z \).

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