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 54.4 cm 54.4 cm 59.5 cm 59.5 cm 46.6 cm 46.6 cm 51.2 cm

Answer 1

To find the length of the diagonal of the rectangular prism, we can use the formula for the diagonal \( d \) of a rectangular prism 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, we can calculate the diagonal \( d \):

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

Calculating the squares:

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

Now, summing these:

\[
d = \sqrt{1024 + 576 + 1936}
\]

Calculating the total:

\[
1024 + 576 + 1936 = 3536
\]

Now, we take the square root:

\[
d = \sqrt{3536}
\]

Calculating the square root gives approximately:

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

Therefore, the length of the diagonal of the rectangular prism, segment \( BE \), is approximately **59.5 cm**.