2014 AMC 10A Problems/Problem 19
Problem
Four cubes with edge lengths , , , and are stacked as shown. What is the length of the portion of contained in the cube with edge length ?
Solution
By Pythagorean Theorem in three dimensions, the distance is .
Let the length of the segment that is inside the cube with side length be . By similar triangles, , giving .
Solution 2 (3D Coordinate Geometry)
Let's redraw the diagram, however make a 3D coordinate plane, using D as the origin.(
Now we can use the distance formula in 3D, which is and plug it in for the distance of .
We get the answer as .
Continuing with solution 1, using similar triangles, we get the answer as
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Video Solution
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See Also
2014 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 18 |
Followed by Problem 20 | |
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