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 B H, is 40 cm. Find the length of the diagonal of the rectangular prism, segment B E. Round the answer to the nearest tenth.
To find the length of the diagonal of the rectangular prism, segment B E, we can use the Pythagorean theorem.
First, we find the length of the diagonal of the base in terms of the length, width, and height of the prism. Let's call the length of segment B E x.
From the right triangle formed by segments B H, H E, and B E, we have:
(B H)^2 + (H E)^2 = (B E)^2
Substitute the known values:
(40)^2 + (24)^2 = x^2
1600 + 576 = x^2
2176 = x^2
Take the square root of both sides to find x:
x = √2176
x ≈ 46.6
Therefore, the length of the diagonal of the rectangular prism, segment B E, is approximately 46.6 cm.