Distance and the Pythagorean Theorem Quick Check
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Question
Use the image to answer the question.
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
4.24
4.24
2.83
2.83
8
8
4
To find the length of the diagonal of the square, we can use the Pythagorean Theorem.
Let x be the length of one side of the square.
Using the Pythagorean Theorem:
diagonal^2 = x^2 + x^2
diagonal^2 = 2x^2
diagonal = sqrt(2x^2) = sqrt(2) * x
Given that one side of the square is 4, we can substitute x=4 into the formula:
diagonal = sqrt(2) * 4 = 4 * sqrt(2) = 5.66 (rounded to the nearest hundredth)
Therefore, the length of the diagonal of the square is approximately 5.66.