Final answer:
The equation y = 4 can be one side of the square if that side is parallel to the x-axis and opposite to the side lying along the x-axis. The Pythagorean theorem can be used to calculate the resultant vector obtained from two perpendicular vectors. The area of a square with sides twice the length of another square is four times greater.
Step-by-step explanation:
Whether the equation y = 4 could be one of the sides of a square placed on the coordinate plane with one corner at the origin and a side length of 4 depends on the orientation of the square. If one side of the square is along the x-axis, starting at the origin (0,0), then the side opposite to it, parallel to the x-axis, would indeed have a constant y-value equal to the length of the side of the square, which is 4. Thus, in such a case, it is true that the equation y = 4 could represent one of the sides of the square.
For the second part of the question, Pythagorean theorem is applicable to calculate the length of the resultant vector which is obtained from the addition of two vectors that are at right angles to each other. So, the statement is true.
Lastly, when comparing the areas of two squares, where one has a side length twice the length of the side of the other, the area of the larger square is four times greater because the area is calculated as the side length squared. Therefore, if the smaller square has a side length of 4 inches, then the larger square has a side length of 8 inches (4 inches x 2), leading to an area calculation of 64 square inches (8 inches x 8 inches), which is four times the area of the smaller square (16 square inches).