How do you calculate the perimeter of a square if its diagonal is 5√2 centimeters?

To find the perimeter of a square when given the length of its diagonal, it is essential to use the properties of a square.

A square's diagonal can be calculated with the formula (d = s\sqrt{2}), where (d) represents the diagonal length and (s) represents the side length of the square. In this case, the diagonal (d) is given as (5\sqrt{2}) centimeters.

Using the formula, we set it up as follows:

[

5\sqrt{2} = s\sqrt{2}

]

To isolate (s), divide both sides by (\sqrt{2}):

[

s = 5 \text{ centimeters}

]

Now that we have the length of one side of the square, we can calculate the perimeter. The perimeter (P) of a square is given by the formula (P = 4s). Substituting in the value of (s):

[

P = 4 \times 5 = 20 \text{ centimeters}

]

Thus, the perimeter of the square is 20 centimeters, which corresponds to the given option.