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 54.4 cm 54.4 cm 51.2 cm 51.2 cm 59.5 cm

1 answer

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

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

where \(l\), \(w\), and \(h\) are the length, width, and height of the prism, respectively.

Given:

  • Length \(l = 32\) cm
  • Width \(w = 24\) cm
  • Height \(h = 44\) cm

Now we can plug in the values:

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

Calculating each term: \[ 32^2 = 1024 \] \[ 24^2 = 576 \] \[ 44^2 = 1936 \]

Now summing these values: \[ 1024 + 576 + 1936 = 3536 \]

Now, take the square root: \[ d = \sqrt{3536} \approx 59.5 \text{ cm} \]

Thus, the length of the diagonal of the rectangular prism, segment BE, rounded to the nearest tenth, is:

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