Question

the length of the prism is 32 cm the with is 24 the height is 44 and the length of the diagonal base bh is 40 find the length of the diagonal of the rectangular prism segment be

Answer 1

To find the length of the diagonal of a rectangular prism, we can use the following formula for the diagonal \(d\):

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

where:
- \(l\) = length,
- \(w\) = width,
- \(h\) = height.

Given:
- \(l = 32 \, \text{cm}\)
- \(w = 24 \, \text{cm}\)
- \(h = 44 \, \text{cm}\)

We can 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 add these values together:

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

Now, we calculate the square root:

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

Thus, the length of the diagonal \(BE\) of the rectangular prism is approximately \(59.5 \, \text{cm}\).