SHOW YOUR WORK: Use the Pythagorean Theorem to find the side length, s, of Square ABCD in feet. (3 points)
The Pythagorean Theorem states that for any right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
In the case of a square, all sides are equal, so we can let s represent the length of each side.
Let's consider a right triangle where the hypotenuse is a diagonal of the square.
If we draw the diagonal, it divides the square into two congruent right triangles.
The two legs of each triangle are s and s, and the hypotenuse is the diagonal, which we'll call d.
According to the Pythagorean Theorem, we have:
s^2 + s^2 = d^2
2s^2 = d^2
Now, we need to find the value of s.
In a square, the diagonal divides the square into two congruent 45-45-90 triangles.
In a 45-45-90 triangle, the ratio of the lengths of the sides is:
1 : 1 : √2
In our case, the hypotenuse of each triangle is s, and one of the legs is s.
Using the ratio, we have:
s : s : s√2
Since the diagonal is the hypotenuse, d = s√2.
Now, we can substitute this value into the Pythagorean Theorem equation:
2s^2 = (s√2)^2
2s^2 = 2s^2
0 = 0
This equation holds true for any value of s.
Therefore, we cannot determine the specific value of s using the given information.
To find the side length of Square ABCD using the Pythagorean Theorem, we need to know the lengths of its sides.
Let's assume that one side of the square is represented by the variable 's'. Since Square ABCD is a square, all of its sides have the same length. So, all four sides of the square are equal to 's'.
According to the Pythagorean Theorem, 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 Square ABCD, the diagonal (the hypotenuse of the right triangle) forms two right triangles with two sides of equal length 's'. Each right triangle has sides 's' (one of the sides of the square) and 's' (one of the sides of the square). The diagonal (the hypotenuse) is the side length of the square, which we're trying to find.
So, we can use the Pythagorean Theorem to solve for 's':
s² + s² = diagonal²
2s² = diagonal²
To find the side length, let's say 's' is the unknown number. Therefore, we can represent 's' as an unknown variable x.
2x² = diagonal²
Now, we need to know the length of the diagonal to find the side length of the square.
Once you have the length of the diagonal, you can substitute it back into the equation, solve for 'x', and determine the side length 's' of Square ABCD.