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The length of the prism is 32 cm the width is 24 cm the height is 44 cm and the length of the diagnol of the base segment BH is 40 cm find the length of the diagnol of the rectaangular prism segment BE round the answer to the nearest tenth

59.5
46.6
51.2
54.4

3 answers

To find the length of the diagonal segment \( BE \) of the rectangular prism, we can use the 3D distance formula, which is derived from the Pythagorean theorem:

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

where:

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

Given:

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

Now, we can plug in the values into the formula:

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

Calculating each square:

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

Adding these values together:

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

Now, calculating \( \sqrt{3536} \):

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

So, the length of the diagonal of the rectangular prism segment \( BE \) is approximately 59.5 cm, which matches one of the given options.

Final answer: 59.5 cm

you sure

Let's carefully recalculate the diagonal of the rectangular prism step by step to ensure the correctness of the answer.

Length of the Diagonal of the Rectangular Prism

We use the formula for the diagonal \( d \) of a rectangular prism:

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

Given Dimensions

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

Step-by-Step Calculation

  1. Calculate \( l^2 \): \[ (32 , \text{cm})^2 = 1024 , \text{cm}^2 \]

  2. Calculate \( w^2 \): \[ (24 , \text{cm})^2 = 576 , \text{cm}^2 \]

  3. Calculate \( h^2 \): \[ (44 , \text{cm})^2 = 1936 , \text{cm}^2 \]

  4. Sum the squares: \[ 1024 + 576 + 1936 = 3536 , \text{cm}^2 \]

  5. Take the square root: \[ d = \sqrt{3536} \approx 59.5 , \text{cm} \]

Conclusion

After reviewing the calculations again, the diagonal \( d \) of the rectangular prism is confirmed to be approximately 59.5 cm. Thus, my earlier answer stands correct. Thank you for your patience!