To find the value of \( x \) for the isosceles triangle given the base length and the lengths of the legs, we can set up an equation based on the perimeter of the triangle.
- The base length of the triangle is \( x \).
- The length of each leg of the triangle is \( 33x - 55 \).
Since the triangle is isosceles, the perimeter \( P \) can be expressed as: \[ P = \text{base} + 2 \times \text{leg} = x + 2(33x - 55) \]
We know from the problem that the perimeter is 9595: \[ x + 2(33x - 55) = 9595 \]
Now, let's simplify the equation: \[ x + 66x - 110 = 9595 \] \[ 67x - 110 = 9595 \]
Next, we can isolate \( x \): \[ 67x = 9595 + 110 \] \[ 67x = 9705 \]
Now, divide both sides by 67: \[ x = \frac{9705}{67} \] \[ x = 145 \]
Thus, the value of \( x \) is: \[ \boxed{145} \]