Final answer:
To find the perimeter of a square, you need to know the length of one side. The length of one side can be found using the Pythagorean theorem. The perimeter of the square is then calculated by multiplying the length of one side by 4.
Step-by-step explanation:
To find the perimeter of a square, we need to know the length of one side of the square. Since the diagonal of the square is given as 37√2 millimeters, we can use the Pythagorean theorem to find the length of one side. The Pythagorean theorem states that for a right triangle, the square of the length of the hypotenuse (diagonal) is equal to the sum of the squares of the lengths of the other two sides (sides of the square).
Let's assume the length of one side of the square is 'a'. Using the Pythagorean theorem, we have: (a^2) + (a^2) = (37√2)^2. Simplifying this equation, we get: 2a^2 = 37^2 * 2. Dividing both sides by 2, we get: a^2 = 37^2. Taking the square root of both sides, we find: a = 37.
Now that we know the length of one side of the square is 37 millimeters, we can find the perimeter by multiplying the length of one side by 4 (since a square has 4 equal sides). The perimeter of the square is 37 * 4 = 148 millimeters.
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