Question

what is the perimeter of square abcd?
√37 units
4√37 units
28 units
37 units

Explanation:

Step1: Calculate the side length using the distance formula

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).
For points \(A(3,4)\) and \(B(2,-2)\), \(x_1 = 3,y_1 = 4,x_2=2,y_2=-2\).
\(AB=\sqrt{(2 - 3)^2+(-2 - 4)^2}=\sqrt{(-1)^2+(-6)^2}=\sqrt{1 + 36}=\sqrt{37}\)

Step2: Calculate the perimeter of the square

Since it is a square, all sides are equal. The perimeter \(P\) of a square with side length \(s\) is \(P = 4s\).
Here \(s=\sqrt{37}\), so \(P = 4\sqrt{37}\)

Answer:

\(4\sqrt{37}\) units