Use the image to answer the question.

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

Answer 1

To find the length of diagonal BE, we can use the Pythagorean theorem.

Let's label the midpoint of BH as point M. We can see that triangle BMH is a right triangle.

The length of segment BH is 40 cm, and the height CD is 44 cm. So, the length of segment MH can be found using the Pythagorean theorem:

MH^2 = BH^2 - CD^2
MH^2 = 40^2 - 44^2
MH^2 = 1600 - 1936
MH^2 = -336

The result is negative, which means that BH is longer than CD, which is not possible in this prism.

Therefore, the given information is not consistent and we cannot find the length of segment BE based on the information provided.