The Pythagorean Theorem in Three Dimensions Quick Check
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Question
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
46.6 cm
46.6 cm
51.2 cm
51.2 cm
59.5 cm
59.5 cm
54.4 cm
54.4 cm
To find the length of the diagonal of the rectangular prism segment BE, we can use the Pythagorean Theorem.
In the triangle formed by the diagonal BE, the height CD, and the base diagonal BH, we can use the Pythagorean Theorem to find the length of BE.
We know that the length of BH is 40 cm and the height CD is 44 cm.
Using the Pythagorean Theorem, we have:
BE^2 = BH^2 + CD^2
BE^2 = 40^2 + 44^2
BE^2 = 1600 + 1936
BE^2 = 3536
Taking the square root of both sides, we get:
BE ≈ 59.5 cm
Therefore, the length of the diagonal of the rectangular prism segment BE is approximately 59.5 cm.
The correct answer is:
59.5 cm