The line segments of a cube include edges, the diagonals of the faces, and the diagonals through the interior of the cube. Which is the longest? Which is the shortest? Explain.
Answers
Answer:
The diagonal through the interior of the cube is the longest. The hypotenuse is the longest side of a right triangle. The diagonal of the cube is the hypotenuse of a right triangle with legs that are the diagonal of a face and an edge. The edges are the shortest. They are legs of a right triangle with the diagonal of a face as the hypotenuse.
Step-by-step explanation:
Answer:
The diagonal through the interior of the cube represents the longest line segment of the cube.
The edges of the cube represents the shortest side of the cube.
Step-by-step explanation:
In a cube , the line segments are :
edges,
the diagonals of the faces, and
the diagonals through the interior of the cube.
Let the edge be = a
So diagonals of the faces = √2 a
diagonals through the interior of the cube = √a²+a²+a²
=√3a²
=√3 a
It is very evident that :
√3 a > √2 a>a
diagonals through the interior of the cube. >diagonals of the faces>edge
The diagonal through the interior of the cube represents the longest line segment of the cube.
The edges of the cube represents the shortest side of the cube.