Geometry Word Problems: The Pythagorean Theorem

[Jesse]

http://www.purplemath.com/modules/perimetr3.htm
(wooden frame problem, with concrete and crosswire)

End of your solution:

5 = d

Adding a half-meter at either end of the wire, I find that:

each wire should be cut to a length of six meters

I was wondering why the answer is 6 meters, as opposed to 5.5 meters.

[Honeysuckle588]

The half-meter is added to each end. So 5 + 1/2 + 1/2 = 6.

[Jesse]

" Assuming an extra half-meter of wire is used at either end of a cross-wire for anchoring,..."

It states either end, not each end.

[Honeysuckle588]

Interesting. According to one of the online dictionaries that I just consulted, when either is used as an adjective (as in this case) it can mean

1. Any one of two; one or the other: wear either coat.
2. One and the other; each: rings on either hand.

So you interpreted it in the first sense, and I interpreted it in the second.

[Jesse]

Hmm, that's very interesting, I have never seen either used like that (not either, as in either of the definitions! In that case I would think both!). From the context of the problem it seems that it would be "one or the other". I think many people would interpret it that way. I think if each was used, there would be no ambiguity at all. So would there be no valid answer?

Elizabeth would you accept either answer? Or if this question was on a test would you throw it off?

[stapel_eliz]

I take "on either end" to mean "on each of the ends", rather than "on one end or else the other, but not both". But if a student showed his work and could justify his answer, I'd accept it.

This points out a problem with the "translation" of English into math: numbers mean what they mean, but words can be slippery!