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
51.2 cm
51.2 cm
59.5 cm
To find the length of the diagonal of the rectangular prism, segment BE, we can use the Pythagorean theorem.
First, let's find the length of diagonal BH using the Pythagorean theorem. We know that the length of the prism is 32 cm and the width is 24 cm, and we are given that the length of diagonal BH is 40 cm.
Using the Pythagorean theorem, we can write:
BH^2 = length^2 + width^2
BH^2 = (32 cm)^2 + (24 cm)^2
BH^2 = 1024 cm^2 + 576 cm^2
BH^2 = 1600 cm^2
Taking the square root of both sides, we find that BH = √(1600 cm^2) = 40 cm.
Next, we need to find the length of diagonal BE. We can use the same concept and apply it to the heights of the rectangular prism.
Using the Pythagorean theorem, we can write:
BE^2 = BH^2 + height^2
BE^2 = (40 cm)^2 + (44 cm)^2
BE^2 = 1600 cm^2 + 1936 cm^2
BE^2 = 3536 cm^2
Taking the square root of both sides, we find that BE =√(3536 cm^2) ≈ 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