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)
59.5 cm
51.2 cm
46.6 cm
54.4 cm

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, which is given by:

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

where:

  • \(l\) is the length of the prism,
  • \(w\) is the width of the prism,
  • \(h\) is the height of the prism.

In this case:

  • \(l = 32 \text{ cm}\)
  • \(w = 24 \text{ cm}\)
  • \(h = 44 \text{ cm}\)

Now we can substitute the values into the formula:

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

Calculating the squares:

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

Now, adding these values together:

\[ 1024 + 576 + 1936 = 3536 \]

Now, take the square root:

\[ d = \sqrt{3536} \]

Calculating the square root:

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

So, the length of the diagonal of the rectangular prism \(BE\) is approximately \(59.5 \text{ cm}\) when rounded to the nearest tenth.

The correct answer is 59.5 cm.