Answer:
The perimeter of the square is;
[tex]17.89[/tex]
Explanation:
Given the square RSTV with the coordinates given the question.
[tex]R(-1,5),S(-3,1),T(-7,3)\text{ and V(-5,7)}[/tex]
Let us find the length of the sides of the square.
Using the formula for distance between two points;
[tex]\begin{gathered} l=RS=\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2} \\ l=RS=\sqrt[]{(1_{}-5)^2+(-3_{}-(-1)_{})^2} \\ l=RS=\sqrt[]{(-4_{})^2+(-2)^2} \\ l=RS=\sqrt[]{20} \\ l=RS=2\sqrt[]{5} \end{gathered}[/tex]
Recall that the perimeter of a square can be calculated using the formula;
[tex]\begin{gathered} P=4l \\ P=4(2\sqrt[]{5}) \\ P=8\sqrt[]{5} \\ P=17.89 \end{gathered}[/tex]
Therefore, the perimeter of the square is;
[tex]17.89[/tex]
