A room and a spider

Question

A room has the shape of a rectangular cuboid. The edges are 3, 4 and 5 metres. There is a spider in one of the corners. The spider now walks to the corner on the other end of the space diagonal using the shortest possible route. How much distance does the spider travel?

I think the solution is $ \sqrt {5^2+4^2}+3$ metres, but I am unsure.

score 5 · Accepted Answer · answered Oct 01 '14 at 20:21

5

If you "unfold the box" (into what I recall being called a net) as rectangles shaped in a cross (see here for what I mean http://www.11plusforparents.co.uk/Maths/shape9.html), then you can draw the shortest line with a straight rule, and you can work out its length with Pythagoras's theorem.

It turns out that it is not fastest to cross the floor diagonally and then walk up one of the edges.

answered Oct 01 '14 at 20:21

James

5,443

Wow! This was really easy! Thanks! I feel stupid now! – user176791 Oct 01 '14 at 20:25
@user176791 Nah don't feel stupid, sometimes the creative solution slips our minds. – Rustyn Oct 01 '14 at 20:59
I didn't get this through deep math skills or anything, I remembered it from a logic puzzle set I had as a boy. – James Oct 01 '14 at 21:07

A room and a spider

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