The diagonal of a square is 4 square root 2. find the length of a side of the square. How do I do this problem?
Thank you
diagonal = side * √2
To find the length of a side of the square, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the diagonal of the square forms the hypotenuse of a right triangle. Let's assume that the length of a side of the square is "s". Therefore, using the Pythagorean theorem, we can set up the following equation:
s^2 + s^2 = (4√2)^2
Simplifying the equation:
2s^2 = (4√2)^2
2s^2 = 16 * 2
2s^2 = 32
Dividing both sides of the equation by 2:
s^2 = 16
Taking the square root of both sides:
s = √16
Since the square root of 16 can be either positive or negative, we can take the positive square root:
s = 4
Therefore, the length of a side of the square is 4 units.