In triangles `ABC` and `DEF`, `angleC = angleF`, `AC = DF`, and `BC = EF`. If `AB = 2x-1` and `DE=5x-4`, then the value of `x` is:

Options

A. 2
B. 3
C. 4
D. 1

Answer

To solve the problem, we need to establish the relationship between the sides of the triangles based on the information given. Let's go through the steps one by one.

### Step 1: Set up the equation based on triangle properties
Since triangles ABC and DEF are similar (as per the given conditions), the corresponding sides are equal. Thus, we can set up the equation:
\[ AB = DE \]

### Step 2: Substitute the expressions for AB and DE
We know from the problem that:
\[ AB = 2x - 1 \]
\[ DE = 5x - 4 \]
Now we can substitute these into our equation:
\[ 2x - 1 = 5x - 4 \]

### Step 3: Rearrange the equation
To solve for \( x \), we need to rearrange the equation. First, let's move all terms involving \( x \) to one side and constant terms to the other side:
\[ 2x - 5x = -4 + 1 \]
This simplifies to:
\[ -3x = -3 \]

### Step 4: Solve for \( x \)
Now, divide both sides by -3:
\[ x = \frac{-3}{-3} = 1 \]

### Step 5: Conclusion
Thus, the value of \( x \) is:
\[ x = 1 \]