The length of the prism is 32 cm, the width is 24 cm, the height is 44 cm, and the length of the diagonal of the base, segment BH , is 40 cm. Find the length of the diagonal of the rectangular prism, segment BE . Round the answer to the nearest tenth. (1 point) Responses 51.2 cm 51.2 cm 54.4 cm 54.4 cm 46.6 cm 46.6 cm 59.5 cm
To find the length of the diagonal of the rectangular prism, segment BE, we can use the Pythagorean theorem.
Consider the triangle BEH with BE as the hypotenuse, BH as one side, and EH as the other side.
Using the Pythagorean theorem:
BE^2 = BH^2 + EH^2
BE^2 = 40^2 + 24^2
BE^2 = 1600 + 576
BE^2 = 2176
Taking the square root of both sides:
BE = √2176
BE ≈ 46.6 cm
Therefore, the length of the diagonal of the rectangular prism, segment BE, is approximately 46.6 cm. The closest answer is 46.6 cm.