Answer:
\(4\sqrt{74
Step-by-step explanation:
To find the fourth point of the rectangle, you need to determine the point that is diagonally opposite to one of the given points. Let's choose the point (3,0) as a reference.
The diagonal of a rectangle divides it into two congruent right triangles. So, the distance between (3,0) and (-4,-5) represents the diagonal of the rectangle.
Using the distance formula:
\[
\text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
The distance between (3,0) and (-4,-5) is:
\[
\text{Distance} = \sqrt{(-4 - 3)^2 + (-5 - 0)^2} = \sqrt{(-7)^2 + (-5)^2} = \sqrt{49 + 25} = \sqrt{74}
\]
Now, you have the length of the diagonal, and you know the length and width of the rectangle.
The perimeter of a rectangle is \(2 \times (\text{length} + \text{width})\). Since the length and width of the rectangle are the same as the lengths of the sides of the right triangle, we have:
\[
\text{Perimeter} = 2 \times (\text{length} + \text{width}) = 2 \times (\sqrt{74} + \sqrt{74}) = 4\sqrt{74}
\]
So, the perimeter of the rectangle is }\).
