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.

1 answer

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:

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