ANSWER
28.285 units
EXPLANATION
We are given the square EFGH and we need to find the perimeter.
The perimeter of a square is given as:
P = 4 * L
P = 4L
where L = length of the side of the square
To find the length of the side of the square, we have to find the distance between a pair of adjacent vertices of the square.
Let us pick E(0, 5) and F(5, 0).
The distance between the two points is:
[tex]L\text{ = }\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
where (x1, y1) = (0, 5)
(x2, y2) = (5, 0)
Therefore, the length of the square (distance between the two points) is:
[tex]\begin{gathered} L\text{ = }\sqrt[]{(5-0)^2+(0-5)^2}\text{ = }\sqrt[]{5^2+(-5)^2} \\ L\text{ = }\sqrt[]{25\text{ + 25}}\text{ = }\sqrt[]{50} \\ L\text{ = 7.071 units} \end{gathered}[/tex]
Therefore, the perimeter of the square is:
P = 4 * 7.071
P = 28.284 units
