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.

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

51.2 cm
51.2 cm

59.5 cm
59.5 cm

46.6 cm
46.6 cm

54.4 cm

Answer 1

To find the length of the diagonal of the rectangular prism \(BE\), we can use the three-dimensional distance formula. The length of the diagonal \(d\) of a rectangular prism can be calculated using the following formula:

\[ d = \sqrt{l^2 + w^2 + h^2} \]

where:

• \(l\) is the length,
• \(w\) is the width,
• \(h\) is the height.

Given:

• Length \(l = 32 , \text{cm}\),
• Width \(w = 24 , \text{cm}\),
• Height \(h = 44 , \text{cm}\).

Now, we can plug in these values into the formula:

\[ d = \sqrt{(32)^2 + (24)^2 + (44)^2} \]

Calculating each term:

\[ (32)^2 = 1024, \] \[ (24)^2 = 576, \] \[ (44)^2 = 1936. \]

Now summing these values:

\[ 1024 + 576 + 1936 = 3536. \]

Now taking the square root:

\[ d = \sqrt{3536} \approx 59.5 , \text{cm}. \]

Therefore, the length of the diagonal \(BE\) of the rectangular prism is approximately \(59.5 , \text{cm}\).

Thus, the correct response is:

59.5 cm