Using the distance between two points to find the length of the side of the square, it is found that:
- The area is of 50 square units.
- The perimeter is of [tex]20\sqrt{2}[/tex] units.
- Hence, option A is correct.
The distance between two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by:
[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
In this problem, the length of the side of the square can be found as the distance between points G and H, that is, the distance between (0,5) and (-5,0), hence:
[tex]l = \sqrt{(0 - (-5))^2 + (5 - 0)^2} = \sqrt{50} = \sqrt{2 \times 25} = 5\sqrt{2}[/tex]
The area of a square of side length l is given by:
[tex]A = l^2[/tex]
Hence:
[tex]A = (5\sqrt{2})^2 = 50[/tex]
The area is of 50 square units.
The perimeter of a square of side length l is given by:
[tex]P = 4l[/tex]
Hence:
[tex]P = 4(5\sqrt{2}) = 20\sqrt{2}[/tex]
The perimeter is of [tex]20\sqrt{2}[/tex] units.
You can learn more about distance between two points at https://brainly.com/question/18345417
