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.
(1 point)
To find the length of diagonal BE, we can use the Pythagorean theorem. Diagonal BE is the hypotenuse of a right triangle formed by the height (CD), and the diagonal of the base (BH).
First, let's find the length of CD using the Pythagorean theorem:
CD^2 = height^2 + width^2
CD^2 = 44^2 + 24^2
CD^2 = 1936 + 576
CD^2 = 2512
Therefore, CD = √2512 ≈ 50.1 cm
Next, let's find the length of BH using the Pythagorean theorem:
BH^2 = length^2 + width^2
40^2 = 32^2 + 24^2
BH^2 = 1600 - 576
BH^2 = 1024
Therefore, BH = √1024 = 32 cm
Now that we have the lengths of CD and BH, we can find the length of BE:
BE^2 = BH^2 + CD^2
BE^2 = 32^2 + 50.1^2
BE^2 = 1024 + 2510.01
BE^2 = 3534.01
Therefore, BE = √3534.01 ≈ 59.4 cm
So, the length of diagonal BE is approximately 59.4 cm.