To find the length of segment BE, we can use the Pythagorean Theorem.
Since segment BH is the diagonal of the base, we can break it down into its components.
The length of segment AB is 32 cm, and the width of segment BC is 24 cm.
Using these values, we can find the length of segment BH using the Pythagorean Theorem:
BH^2 = AB^2 + BC^2
BH^2 = 32^2 + 24^2
BH^2 = 1024 + 576
BH^2 = 1600
BH = 40 cm
Now, we can use the length of BH and the height of the prism to find the length of BE.
Segment BH is the hypotenuse of the right triangle formed by segments BH and EH.
Segment EH is the height of the prism (44 cm).
Using the Pythagorean Theorem again, we can find the length of segment BE:
BE^2 = BH^2 + EH^2
BE^2 = 40^2 + 44^2
BE^2 = 1600 + 1936
BE^2 = 3536
BE ≈ 59.5 cm (to the nearest tenth)
Therefore, the length of the diagonal of the rectangular prism, segment BE, is approximately 59.5 cm.
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 answer
1 answer