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

Question

, is 40 cm. Find the length of the diagonal of the rectangular prism, segment BE
. Round the answer to the nearest tenth.

(1 point)
Responses

54.4 cm
54.4 cm

51.2 cm
51.2 cm

46.6 cm
46.6 cm

59.5 cm

Answer 1

To find the length of the diagonal of the rectangular prism (segment BE), 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,
• $w$ is the width,
• $h$ is the height.

In this case:

• Length $l=32,\text{cm}$
• Width $w=24,\text{cm}$
• Height $h=44,\text{cm}$

Substituting these values into the formula:

$$D=\sqrt{{32}^2+{24}^2+{44}^2}$$ $$=\sqrt{1024+576+1936}$$ $$=\sqrt{3536}$$

Now, we calculate the square root:

$$D\approx 59.5,\text{cm}$$

Thus, the length of the diagonal of the rectangular prism (segment BE) is approximately 59.5 cm.