The length of a diagonal of a square is 37√2 millimeters. find the perimeter of the square

The answer is 148.

Step-by-step explanation:

Because it is a square, the sides are equal. Taking half the square, you have a right triangle with sides that are equal with a hypotenuse of 37√2.

The equation a^2 + b^2 = c^2 applies.

In this case sides a and b are equal, so we can substitute a for b. The following equation applies:

a^2 + a^2 = c^2

2a^2 = c^2

Substitute in the value of C:

2a^2 = (37√2) ^2

2a^2 = 1369 * 2

Divide both sides by 2

a^2 = 1369

Take the square root of both sides:

a = 37

Each side is 37 units. The perimeter is 37 * 4 = 148 units.