In a right triangle with sides 3, 4, and 5 feet,
a bug starts at the vertex of the right angle
and crawls straight (perpendicular) toward the opposite side.
Then it turns and crawls straight towards the closer opposite side.
If it keeps turning and crawling to the closer side indefinitely,
what total distance does the bug crawl?
[SECRET]
Q: 삼각형을 영어로 쓰면?
A:triangle
[solution]
The first part of the bug's trip divides the triangle into two similar triangles,
one 4/5 the original size, the other 3/5 the original size.
This first part is thus 4/5(3)=3/5(4)=12/5 feet long,
and each succeeding part will divide the triangle as before
(using 3/5 since that side is nearer).
So the total distance is an infinite sum
S=12/5+12/5(3/5)+12/5(3/5)(3/5)+....
Then (3/5)S=S-12/5, so solving gives S=6 feet.
This is accomplished in finite time if the bug maintains its speed.
[/SECRET]
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