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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.

Answer 1

To find the length of the diagonal of the rectangular prism, segment \( BE \), we use the formula for the diagonal \( D \) of a rectangular prism, which is given by:

\[ D = \sqrt{L^2 + W^2 + H^2} \]

where \( L \) is the length, \( W \) is the width, and \( H \) is the height of the prism.

Given:

• Length \( L = 32 \) cm
• Width \( W = 24 \) cm
• Height \( H = 44 \) cm

Now, substituting these values into the formula:

\[ D = \sqrt{32^2 + 24^2 + 44^2} \]

Now, we calculate each term:

\[ 32^2 = 1024 \] \[ 24^2 = 576 \] \[ 44^2 = 1936 \]

Next, we sum these values:

\[ D = \sqrt{1024 + 576 + 1936} \] \[ D = \sqrt{3536} \]

Now, we calculate the square root:

\[ D \approx 59.5 \text{ cm} \]

Thus, the length of the diagonal of the rectangular prism, segment \( BE \), rounded to the nearest tenth, is

\[ \boxed{59.5} \text{ cm} \]