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
54.4 cm
54.4 cm
51.2 cm
51.2 cm
59.5 cm
59.5 cm
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To find the length of the diagonal of the rectangular prism, segment BE, we can use the Pythagorean theorem.
We know that the length of the base, segment AB, is 32 cm and the width, segment BC, is 24 cm. Since BH is the diagonal of the base, it forms a right triangle with sides AB and BC. Therefore, we can use the Pythagorean theorem to find the length of BH.
The formula for the length of a diagonal in a rectangle is √(length^2 + width^2).
Plugging in the values, we have √(32^2 + 24^2) = √(1024 + 576) = √1600 = 40 cm.
Now we need to find the length of the diagonal of the prism, segment BE. Using the same logic, BE forms a right triangle with sides BH and the height, segment CD. Therefore, we can use the Pythagorean theorem again to find the length of BE.
The formula for the length of a diagonal in a rectangular prism is √(diagonal of base^2 + height^2).
Plugging in the values, we have √(40^2 + 44^2) = √(1600 + 1936) = √(3536) ≈ 59.5 cm.
Therefore, the length of the diagonal of the rectangular prism, segment BE, is approximately 59.5 cm.
So, the correct answer is 59.5 cm.