The Pythagorean Theorem in Three Dimensions Quick Check 2 of 52 of 5 Items Question Use the image to answer the question. 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 46.6 cm 46.6 cm 51.2 cm 51.2 cm 54.4 cm 54.4 cm 59.5 cm
To find the length of the diagonal of the rectangular prism, segment BE, we can use the Pythagorean Theorem.
First, let's find the length of segment HE.
HE = √(32^2 + 24^2)
HE = √(1024 + 576)
HE = √1600
HE = 40 cm
Now, we can find the length of segment BE using the Pythagorean Theorem in the triangle BEH.
BE = √(40^2 + 44^2)
BE = √(1600 + 1936)
BE = √3536
BE ≈ 59.5 cm
Therefore, the length of segment BE, the diagonal of the rectangular prism, is approximately 59.5 cm.
The correct response is: 59.5 cm