Using Pythagorean theorem to find the side length , s, of a square ABCD in feet.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In the case of a square, all sides are equal in length. Let's call the length of one side of the square "s".
Now, let's draw a right triangle within the square. The hypotenuse of this triangle would be the diagonal of the square. The other two sides of the right triangle would be two adjacent sides of the square.
Using the Pythagorean theorem, we can write the following equation:
s^2 + s^2 = (diagonal of the square)^2
Since the diagonal of a square is equal to the square root of 2 times one of its sides, we can simplify the equation as:
2s^2 = (sqrt(2) * s)^2
Expanding the equation further gives:
2s^2 = 2 * s^2
Since the right side of the equation is equal to the left side, we can conclude that:
2s^2 = 2s^2
This equation holds true for all values of s, which means there is no specific side length of the square that satisfies the Pythagorean theorem.