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
51.2 cm
51.2 cm
59.5 cm
59.5 cm
46.6 cm
46.6 cm
54.4 cm
To find the length of the diagonal of the rectangular prism, segment BE, we can use the Pythagorean Theorem. Since triangle BHE is a right triangle, we can use the lengths of BH and HE to find the length of BE.
BH, the length of the diagonal of the base, is given as 40 cm. And since BE is an extension of BH, it is also equal to 40 cm.
To find HE, we can use the lengths of the sides of the rectangular prism that are perpendicular to HE. HE is perpendicular to both BC (width) and CD (height). So, we can use the Pythagorean theorem to find HE.
BC (width) is given as 24 cm, and CD (height) is given as 44 cm.
Using the Pythagorean Theorem, we have:
HE^2 = BC^2 + CD^2
HE^2 = 24^2 + 44^2
HE^2 = 576 + 1936
HE^2 = 2512
Taking the square root of both sides, we find:
HE ≈ √2512
HE ≈ 50.1 cm
Finally, we can use the lengths of BH and HE to find the length of BE using the Pythagorean Theorem:
BE^2 = BH^2 + HE^2
BE^2 = 40^2 + 50.1^2
BE^2 = 1600 + 2510.01
BE^2 ≈ 4110.01
Taking the square root of both sides, we find:
BE ≈ √4110.01
BE ≈ 64.1 cm
Rounding to the nearest tenth, the length of the diagonal of the rectangular prism, segment BE, is approximately 64.1 cm. Therefore, the correct answer is 64.1 cm.
girl bye choose the best answer
Apologies for the confusion. The best answer is 59.5 cm, as it is the closest rounded value to the correct answer of approximately 64.1 cm.
To find the length of the diagonal of the rectangular prism, segment BE, we can use the Pythagorean theorem.
In the given diagram, we have the following measurements:
- Length (AB) = 32 cm
- Width (BC) = 24 cm
- Height (CD) = 44 cm
- Diagonal of the base (BH) = 40 cm
First, we need to find the length of diagonal BE. To do this, we can consider the right triangle BCE. The base EC is equal to the width (24 cm), the height BC is equal to the height (44 cm), and we need to find the hypotenuse BE (diagonal).
Using the Pythagorean theorem, we have:
BE^2 = BC^2 + EC^2
BE^2 = 24^2 + 44^2
BE^2 = 576 + 1936
BE^2 = 2512
To find BE, we need to take the square root of both sides:
BE ≈ √2512
BE ≈ 50.1 cm
Therefore, the length of the diagonal of the rectangular prism, segment BE, is approximately 50.1 cm. Rounding to the nearest tenth, the answer is 50.1 cm.