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 , is 40 cm. Find
the length of the diagonal of the
rectangular prism, segment .
Round the answer to the nearest
tenth.

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 its length \( l \), width \( w \), and height \( h \):

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

Given:
- Length \( l = 32 \) cm
- Width \( w = 24 \) cm
- Height \( h = 44 \) cm

Now, we can plug the values into the formula:

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

Calculating each term inside the square root:

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

Now, sum these squares:

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

Now, we calculate \( \sqrt{3536} \):

\[
\sqrt{3536} \approx 59.5
\]

So, the length of the diagonal of the rectangular prism, rounded to the nearest tenth, is:

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