Apply the Pythagorean theorem to find the length of the diagonal of the square round your answer to the nearest hundredth if necessary

Answer 1

The Pythagorean theorem states that for 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 four sides are equal in length. Let's assume that each side of the square has a length of "s".

To find the length of the diagonal (the hypotenuse) of the square, we can draw a right triangle inside the square by connecting two opposite corners of the square.

The two shorter sides of the right triangle are the sides of the square (each with length "s"), and the diagonal is the hypotenuse. By using the Pythagorean theorem, we can find the length of the diagonal:

(diagonal)^2 = (side1)^2 + (side2)^2
(d)^2 = s^2 + s^2
(d)^2 = 2s^2

To find "d" (the length of the diagonal), we take the square root of both sides:

d = √(2s^2)
d = √2(s)

So, the length of the diagonal of a square is given by the formula d = √2(s).

Rounding to the nearest hundredth if necessary, we would have to know the length of one side of the square (s) in order to calculate the length of the diagonal (d).