The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In this case, let's consider a square with side length "s" and a diagonal "d".
We can draw a right triangle by connecting one corner of the square to the midpoint of one side. The two sides of the triangle will be the length of one side of the square ("s") and half the length of the diagonal ("d/2").
According to the Pythagorean Theorem, we have:
(s)^2 + (d/2)^2 = d^2
Expanding this equation, we get:
s^2 + d^2/4 = d^2
Combining like terms, we have:
s^2 = 3d^2/4
Multiplying both sides by 4/3, we get:
4s^2/3 = d^2
Taking the square root of both sides, we get:
sqrt(4s^2/3) = d
Simplifying this equation, we have:
(2s/√3) = d
Therefore, the length of the diagonal of the square is given by (2s/√3), where "s" is the length of one side of the square.
Apply the Pythagorean Theorem to find the length of the diagonal of the square. Round your answer to the nearest hundredth, if necessary.
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