Show a complete solution to each problem.

Find the exact length of the side of a square whose diagonal is 3 feet.

I am having problems understanding how you figure out this problem. Can someone help me? Thanks.

Draw a square. Draw a diagonal. Let each side length be x.

The Pythagorean theorem tells you that x^2 + x^2 = 2x^2 = 3^2 = 9
Solve for x.

To find the exact length of the side of a square whose diagonal is 3 feet, we can use the Pythagorean theorem.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (in this case, the diagonal) is equal to the sum of the squares of the lengths of the other two sides (in this case, the sides of the square).

For a square, all sides have equal length. Let's say the length of each side of the square is x.

Using the Pythagorean theorem, we have:

x^2 + x^2 = 3^2

Simplifying, we get:

2x^2 = 9

Dividing both sides by 2, we have:

x^2 = 4.5

Taking the square root of both sides, we get:

x = √4.5

x ≈ 2.1213 (rounded to four decimal places)

So, the exact length of each side of the square is approximately 2.1213 feet.