Pole in a Box
Date: 02/09/99 at 18:18:07 From: Anonymous Subject: Pythagoras A removal truck comes to pick up a pole of length 6.5m. The dimensions of the truck are 3m, 3.5m, and 4m. Will the pole fit in the truck? Thank you.
Date: 02/09/99 at 18:38:11 From: Doctor Wilkinson Subject: Re: Pythagoras I think you're supposed to think of the part of the truck not counting the wheels and the cab where the driver sits and so on, like a big box, say 4m long, 3m wide, and 3.5 m high. (It doesn't really matter which dimension is which). To get a really long object into the truck, you want to angle it so that it goes from one corner on the floor to the opposite corner on the ceiling. So the question is, how far is it from one corner on the floor to the opposite corner on the ceiling? To figure this out, we use Pythgoras's Theorem twice. First of all, we can figure out the length of the diagonal of the floor of the truck. It's 3 feet wide and 4 feet long, so it's 5 feet on the diagonal, using the well-known 3-4-5 right triangle (3 squared plus four squared = 5 squared). Now you get another right triangle if you take the diagonal as one side and the height of the truck from one end of the diagonal to the ceiling as the other. So we have a right triangle with one side of 5 and one side of 3.5. We can find the hypotenuse by Pythagoras's Theorem: the square of the hypotenuse is 3.5 squared + 5 squared, which is 37.25. This is less than 6.5 squared, so the pole will not fit. - Doctor Wilkinson, The Math Forum http://mathforum.org/dr.math/
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