Competition problem — Geometry — Maths Olympiad Prep

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Geometry Difficulty 2.3 Junior Find the answer

Four cubes with edge lengths $1$ , $2$ , $3$ , and $4$ are stacked as shown. What is the length of the portion of $\overline{XY}$ contained in the cube with edge length $3$ ?

Pick one

Solution

By Pythagorean Theorem in three dimensions, the distance $XY$ is $\sqrt{4^2+4^2+10^2}=2\sqrt{33}$ .
Let the length of the segment $XY$ that is inside the cube with side length $3$ be $x$ . By similar triangles, $\dfrac{x}{3}=\dfrac{2\sqrt{33}}{10}$ , giving $x=\boxed{\textbf{(A) }\dfrac{3\sqrt{33}}{5}} skr-$ .

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.