find the length of the diagonal of a rectangular prism with dimensions, in centimeters, of 36 by 48 by 91
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 square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the diagonal of the rectangular prism is the hypotenuse of a right triangle, and the sides of the triangle are the three dimensions of the prism.
Let's call the length, width, and height of the prism as a, b, and c, respectively.
Using the Pythagorean theorem, we have:
diagonal^2 = a^2 + b^2 + c^2
In this case, a = 36 cm, b = 48 cm, and c = 91 cm.
Substituting these values into the equation, we get:
diagonal^2 = 36^2 + 48^2 + 91^2
diagonal^2 = 1296 + 2304 + 8281
diagonal^2 = 11881
Taking the square root of both sides to solve for diagonal, we have:
diagonal = √11881
diagonal ≈ 109 cm
Therefore, the length of the diagonal of the rectangular prism is approximately 109 centimeters.