Use the image to answer the question.
An illustration of a rectangular prism is shown with labeled parts. The left and back base edges are not visible but their positions are indicated by a dashed line. The 6 vertices are labeled A B C D E F and G. The base edge A B is labeled length. Base edge B C is labeled width. The perpendicular C D is labeled height. A dotted line crosses the rectangular base through the center to show diagonal B H. A dashed line extends up from the base indicating the left rear perpendicular E H. A dotted line crosses from the back top left vertex E to the front bottom right vertex B to show diagonal B E. This dotted line is labeled diagonal.
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
59.5 cm
59.5 cm
54.4 cm
54.4 cm
51.2 cm
51.2 cm
46.6 cm
46.6 cm
just choose one of the answers dont need to explain
Based on the given information and the provided illustration of the rectangular prism, we can find the length of the diagonal of the rectangular prism, segment BE.
First, we need to find the length of segment BE by using the Pythagorean theorem.
In the illustration, segment BH represents the diagonal of the base, and it is given as 40 cm. Segment EH represents the height, which is perpendicular to BH. Thus, triangle BEH is a right triangle.
Using the Pythagorean theorem, we can find the length of segment BE.
BE^2 = BH^2 + EH^2
BE^2 = 40^2 + 44^2 (Substituting the given values)
BE^2 = 1600 + 1936
BE^2 = 3536
BE ≈ sqrt(3536) ≈ 59.5 cm (Rounded to the nearest tenth)
Therefore, the length of the diagonal of the rectangular prism, segment BE, is approximately 59.5 cm.