find the length of the diagonal of a rectangular prism with dimensions, in centimeters, of 4 by 5 by 7
To find the length of the diagonal of a rectangular prism, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the hypotenuse (the longest side).
In this case, the diagonal is the hypotenuse of a right triangle formed by the three dimensions of the rectangular prism.
Using the Pythagorean theorem, we can calculate the length of the diagonal as follows:
d^2 = 4^2 + 5^2 + 7^2
d^2 = 16 + 25 + 49
d^2 = 90
Taking the square root of both sides, we get:
d = √90
d ≈ 9.49
Therefore, the length of the diagonal of the rectangular prism is approximately 9.49 centimeters.