what is the length of the space diagonal in the rectangular prism. 12 in, 3 in, 4 in.
To find the length of the space diagonal in a rectangular prism, you can use the Pythagorean theorem. The space diagonal is the line segment that connects two opposite corners of the rectangular prism.
Using the given dimensions of the rectangular prism, we can label the sides as follows:
Length = 12 inches
Width = 3 inches
Height = 4 inches
The space diagonal is the hypotenuse of a right triangle formed by the three dimensions. We can find the length of the diagonal using the Pythagorean theorem:
diagonal^2 = length^2 + width^2 + height^2
diagonal^2 = 12^2 + 3^2 + 4^2
diagonal^2 = 144 + 9 + 16
diagonal^2 = 169
Taking the square root of both sides:
diagonal = √169
diagonal = 13
Therefore, the length of the space diagonal in the rectangular prism is 13 inches.