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, a segment BH, is 40 cm. Find the length of the diagonal of the rectangular prism, segment. BE. Round your answer to the nearest 10th. The available responses are: 54.4. cm. 46.6 cm. 59.5 cm. Or 51.2 cm
To find the length of the diagonal of the rectangular prism (segment BE), we can use the Pythagorean theorem.
First, let's find the length of the diagonal of the base, segment HE:
HE^2 = HB^2 + BE^2
HE^2 = 40^2 + 24^2
HE^2 = 1600 + 576
HE^2 = 2176
HE = √2176
HE ≈ 46.6 cm
Now, let's find the length of the diagonal of the rectangular prism, segment BE:
BE^2 = HE^2 + HB^2
BE^2 = 46.6^2 + 32^2
BE^2 = 2171.56 + 1024
BE^2 = 3195.56
BE = √3195.56
BE ≈ 56.5 cm
Therefore, the length of the diagonal of the rectangular prism, segment BE, is approximately 56.5 cm. So, the closest available response is 59.5 cm.