Answer:
D. by squaring one side length and doubling the value; then taking the square root of that value
Step-by-step explanation:
Multiplying the length of the square by itself gets you the area of the square, so A is incorrect.
Adding the lengths of all four sides of the square gets you the perimeter of the square, so B is incorrect.
Multiplying 1/2 by the length of the base times the height would get you the area of half of the square, so C is incorrect.
What you need to do is use the Pythagorean theorem: [tex]a^2 + b^2 = c^2[/tex]. This formula means that the legs of a right triangle squared and added together will equal the diagonal side squared. Since the side lengths of a square are all the same, we can simplify the formula into [tex]2a^2 = c^2[/tex]. When we solve that equation for the diagonal, we get [tex]c = \sqrt{2a^2}[/tex], which is what answer D describes. Therefore, D is correct.
