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
54.4 cm
54.4 cm
59.5 cm
59.5 cm
To find the length of the diagonal of the rectangular prism, segment BE, we can use the Pythagorean theorem.
Let's label the length of segment BE as x. We can form a right triangle with segment BC, segment BH, and segment HC. Since segment BH is the diagonal of the base, it forms a right angle with segment BC and HC.
Using the Pythagorean theorem, we have:
BC^2 + HC^2 = BH^2
Substituting in the given values, we have:
24^2 + 44^2 = 40^2
576 + 1936 = 1600
2512 = 1600
Now, we can find the length of segment HC by subtracting the heights of segments BH and BC:
HC = 44 - 32
HC = 12
Now, we can solve for BC:
BC^2 + 12^2 = 40^2
BC^2 + 144 = 1600
BC^2 = 1456
BC ≈ 38.1
Finally, we can find the length of segment BE by using the Pythagorean theorem again:
BE^2 = BC^2 + BH^2
BE^2 = 38.1^2 + 40^2
BE^2 ≈ 1453.61 + 1600
BE^2 ≈ 3053.61
BE ≈ √3053.61
BE ≈ 55.3
Rounding to the nearest tenth, the length of the diagonal of the rectangular prism, segment BE, is approximately 55.3 cm.
So the correct answer is not in the given options.