The perimeter of a triangle with vertices (0,4),(0,0) and (3,0) is

Options

A. `5`
B. `12`
C. `11`
D. `7+sqrt(5)`

Explanation

To find the perimeter of the triangle with vertices at (0, 4), (0, 0), and (3, 0), we will calculate the lengths of each side of the triangle and then sum them up.

### Step 1: Identify the vertices
The vertices of the triangle are:
- A (0, 4)
- O (0, 0)
- B (3, 0)

### Step 2: Calculate the lengths of the sides
We will calculate the lengths of the sides OA, OB, and AB.

1. **Length of OA**:
- Points O (0, 0) and A (0, 4) are on the same vertical line.
- The length OA = |y2 - y1| = |4 - 0| = 4 units.

2. **Length of OB**:
- Points O (0, 0) and B (3, 0) are on the same horizontal line.
- The length OB = |x2 - x1| = |3 - 0| = 3 units.

3. **Length of AB**:
- To find the length of AB, we can use the distance formula:
\[ AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
- Here, A (0, 4) and B (3, 0):
\[ AB = \sqrt{(3 - 0)^2 + (0 - 4)^2} = \sqrt{3^2 + (-4)^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \text{ units} \]

### Step 3: Calculate the perimeter
The perimeter P of the triangle is the sum of the lengths of its sides:
\[ P = OA + OB + AB = 4 + 3 + 5 = 12 \text{ units} \]

### Final Answer
The perimeter of the triangle is **12 units**.

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