F

diagonal
A
--.
length
G
D
height
C
width
B
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)
51.2 cm
46.6 cm
59.5 cm
54.4 cm

1 answer

To find the length of the diagonal \( BE \) 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,
  • \( h \) is the height.

From the information provided:

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

Now we will substitute these values into the formula:

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

Calculating each term:

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

Now, summing these values:

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

Now, we can compute the square root of \( 3536 \):

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

Thus, the length of the diagonal \( BE \) of the rectangular prism is approximately \( 59.5 \) cm. Rounding to the nearest tenth, we get:

\[ \text{The answer is } 59.5 \text{ cm.} \]