Use the image to answer the question.
An illustration of a rectangular prism is shown with labeled parts. The left and back base edges are not visible but their positions are indicated by a dashed line. The 6 vertices are labeled A B C D E F and G. The base edge A B is labeled length. Base edge B C is labeled width. The perpendicular C D is labeled height. A dotted line crosses the rectangular base through the center to show diagonal B H. A dashed line extends up from the base indicating the left rear perpendicular E H. A dotted line crosses from the back top left vertex E to the front bottom right vertex B to show diagonal B E. This dotted line is labeled diagonal.
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.
We can use the Pythagorean theorem to find the length of segment BE.
First, let's find the length of segment BH, which is the diagonal of the rectangular base. Since we have the length and width of the base, we can use the Pythagorean theorem to find BH.
The length of the base, AB, is 32 cm, and the width of the base, BC, is 24 cm. Using the Pythagorean theorem, we have:
BH^2 = AB^2 + BC^2
BH^2 = 32^2 + 24^2
BH^2 = 1024 + 576
BH^2 = 1600
BH = √1600
BH = 40 cm
Now, let's find the length of segment BE. This is the diagonal of the rectangular prism.
We can use the Pythagorean theorem again, this time using the height of the prism (CD) and the length of segment BH.
BE^2 = BH^2 + CD^2
BE^2 = 40^2 + 44^2
BE^2 = 1600 + 1936
BE^2 = 3536
BE = √3536
BE ≈ 59.4 cm
Therefore, the length of the diagonal of the rectangular prism, segment BE, is approximately 59.4 cm.