ABCD is a rectangle whose vertices are B(4,0), C(4, 3) and D(0, 3). The length of one of its diagonals is:

Options

A. 4
B. 5
C. 3
D. 25

Answer

To find the length of one of the diagonals of rectangle ABCD, we will use the distance formula. The vertices of the rectangle are given as follows:

- B(4, 0)
- C(4, 3)
- D(0, 3)

First, we need to identify the coordinates of point A. Since ABCD is a rectangle, we can determine the coordinates of A based on the coordinates of the other points.

1. **Identify the coordinates of point A:**
- Since B is at (4, 0) and D is at (0, 3), point A will be at (0, 0).
- Therefore, the coordinates of point A are A(0, 0).

2. **Choose a diagonal to calculate its length:**
- We can choose diagonal BD or AC. Let's calculate the length of diagonal BD.

3. **Apply the distance formula:**
- The distance formula is given by:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
- For diagonal BD, we have:
- B(4, 0) → (x1, y1) = (4, 0)
- D(0, 3) → (x2, y2) = (0, 3)

4. **Substitute the coordinates into the distance formula:**
\[ d = \sqrt{(0 - 4)^2 + (3 - 0)^2} \]

5. **Calculate the squares:**
\[ d = \sqrt{(-4)^2 + (3)^2} = \sqrt{16 + 9} \]

6. **Add the squares:**
\[ d = \sqrt{25} \]

7. **Take the square root:**
\[ d = 5 \]

Thus, the length of one of the diagonals (BD) is **5 units**.