To find the value of \(x\), we start by writing the equation for the perimeter of the isosceles triangle.
The perimeter \(P\) of the triangle can be expressed as:
\[ P = \text{base} + 2 \times \text{leg} \]
In your case, the base is \(x\), and each leg is \(33x - 55\). Therefore, the perimeter can be written as:
\[ P = x + 2(33x - 55) \]
We are given that the perimeter is 9595, so we set up the following equation:
\[ x + 2(33x - 55) = 9595 \]
Now, we can simplify and solve for \(x\):
- Distribute the 2:
\[ x + 66x - 110 = 9595 \]
- Combine like terms:
\[ 67x - 110 = 9595 \]
- Add 110 to both sides:
\[ 67x = 9595 + 110 \] \[ 67x = 9705 \]
- Finally, divide by 67:
\[ x = \frac{9705}{67} \]
Calculating the division:
\[ x = 145 \]
The value of \(x\) is \(145\).