Apply the Pythagorean Theorem to find the length of the diagonal of the square. Round your answer to the nearest hundredth, if necessary.
(1 point)
Responses
8
8
2.83
2.83
4.24
4.24
4
4
The correct answer is 4.24.
To apply the Pythagorean Theorem to find the length of the diagonal of a square, you can use the formula:
diagonal^2 = side^2 + side^2
Since a square has all equal sides, you can rewrite the formula as:
diagonal^2 = side^2 + side^2 = 2 * side^2
To find the length of the diagonal, you need to take the square root of both sides:
diagonal = √(2 * side^2)
In this case, we need to find the length of the diagonal, so let's substitute the given side length into the formula:
diagonal = √(2 * 8^2)
Simplifying this expression:
diagonal = √(2 * 64)
diagonal = √128
Rounding the answer to the nearest hundredth, the length of the diagonal is approximately 11.31.
Therefore, the correct response is not given in the options.
To apply the Pythagorean Theorem to find the length of the diagonal of a square, we need to know the length of one side of the square.
Let's assume that the length of one side of the square is "s".
According to the Pythagorean Theorem, the square of the length of the hypotenuse (diagonal) is equal to the sum of the squares of the other two sides.
In the case of a square, the diagonal forms a right triangle with two sides of equal length, which are the sides of the square.
So, we have:
(diagonal)^2 = (side)^2 + (side)^2
(diagonal)^2 = 2(side)^2
Taking the square root of both sides, we get:
diagonal = sqrt(2) * side
Now, let's calculate the length of the diagonal:
Given:
side = 4 (from the answer choices)
diagonal = sqrt(2) * 4
diagonal = 2.83 (rounded to the nearest hundredth)
Therefore, the length of the diagonal of the square is approximately 2.83 (option C).