A triangle is formed by the x axis and the lines 2x + y = 4 and x-y+1 = 0 as three sides. Taking the side along x-axs as Its base, the corresponding altitude of the triangle is :

Options

A. 2 unit
B. 3 unit
C. `sqrt5` unit
D. 1 unit

Answer

To find the corresponding altitude of the triangle formed by the x-axis and the lines \(2x + y = 4\) and \(x - y + 1 = 0\), we can follow these steps:

### Step 1: Find the intersection points of the lines with the x-axis
1. **For the line \(2x + y = 4\)**:
- Set \(y = 0\) to find the x-intercept.
- \(2x + 0 = 4 \Rightarrow 2x = 4 \Rightarrow x = 2\).
- So, the point is \((2, 0)\).

2. **For the line \(x - y + 1 = 0\)**:
- Set \(y = 0\) to find the x-intercept.
- \(x - 0 + 1 = 0 \Rightarrow x + 1 = 0 \Rightarrow x = -1\).
- So, the point is \((-1, 0)\).

### Step 2: Find the intersection point of the two lines
To find the height of the triangle, we need to find the intersection point of the two lines.

1. **The equations of the lines are**:
- \(2x + y = 4\) (Equation 1)
- \(x - y + 1 = 0\) can be rewritten as \(y = x + 1\) (Equation 2)

2. **Substituting Equation 2 into Equation 1**:
\[ 2x + (x + 1) = 4 \]
\[ 2x + x + 1 = 4 \]
\[ 3x + 1 = 4 \]
\[ 3x = 3 \Rightarrow x = 1 \]

3. **Substituting \(x = 1\) back into Equation 2 to find \(y\)**:
\[ y = 1 + 1 = 2 \]
- So, the intersection point is \((1, 2)\).

### Step 3: Determine the altitude of the triangle
The altitude of the triangle is the y-coordinate of the intersection point, which is \(2\).

### Conclusion
The corresponding altitude of the triangle is \(2\) units.