2015 AMC 8 Problems/Problem 12
Contents
Problem
How many pairs of parallel edges, such as and or and , does a cube have?
Solutions
Solution 1
We first count the number of pairs of parallel lines that are in the same direction as . The pairs of parallel lines are , , , , , and . These are pairs total. We can do the same for the lines in the same direction as and . This means there are total pairs of parallel lines.
Solution 2
Look at any edge, let's say . There are three ways we can pair with another edge. , , and . There are 12 edges on a cube. 3 times 12 is 36. We have to divide by 2 because every pair is counted twice, so is total pairs of parallel lines.
Solution 3
We can use the feature of 3-Dimension in a cube to solve the problem systematically. For example, in the 3-D of the cube, , , and have different parallel edges respectively. So it gives us the total pairs of parallel lines are .
--LarryFlora
Video Solution
https://youtu.be/Zhsb5lv6jCI?t=1306
Video Solution 2
~savannahsolver
See Also
2015 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 11 |
Followed by Problem 13 | |
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All AJHSME/AMC 8 Problems and Solutions |
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