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)
Responses
54.4 cm
54.4 cm
46.6 cm
46.6 cm
59.5 cm
59.5 cm
51.2 cm
51.2 cm
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page 15 of 15
To find the length of segment BE, we can use the Pythagorean theorem.
First, we need to find the length of segment EH. Let's call it x. We can use the Pythagorean theorem with the known sides length (width) = 24 cm and height = 44 cm.
x^2 = 24^2 + 44^2
x^2 = 576 + 1936
x^2 = 2512
Now, let's find the length of segment BH. It is given as 40 cm.
Now, we can use the Pythagorean theorem again to find the length of the segment BE.
BE^2 = BH^2 + EH^2
BE^2 = 40^2 + 2512
BE^2 = 1600 + 2512
BE^2 = 4112
Now, we can find the square root of 4112 to get the length of BE.
BE = √4112
BE ≈ 64.1 cm
Rounded to the nearest tenth, the length of segment BE is approximately 64.1 cm.
Therefore, none of the given answer choices is correct.