Rectangle Diagonal 483A69

1. **State the problem:** We have a rectangle AOBC with vertices A(0,3), O(0,0), and B(5,0). We need to find the length of its diagonals. 2. **Identify the fourth vertex:** Since AOBC is a rectangle, the fourth vertex C must be at (5,3) to complete the rectangle. 3. **Formula for diagonal length:** The diagonal length $d$ of a rectangle with vertices $(x_1,y_1)$ and $(x_2,y_2)$ is given by the distance formula: $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ 4. **Calculate the diagonal length:** The diagonal connects vertices O(0,0) and C(5,3). Substitute these coordinates: $$d = \sqrt{(5 - 0)^2 + (3 - 0)^2} = \sqrt{5^2 + 3^2} = \sqrt{25 + 9} = \sqrt{34}$$ 5. **Result:** The length of the diagonals of rectangle AOBC is $$\sqrt{34}$$ units.