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### Geometry Word Problems: The Pythagorean Theorem

Posted: **Fri Jul 17, 2009 12:07 am**

by **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.

### Re: Geometry Word Problems: The Pythagorean Theorem

Posted: **Fri Jul 17, 2009 4:18 am**

by **Honeysuckle588**

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

### Re: Geometry Word Problems: The Pythagorean Theorem

Posted: **Fri Jul 17, 2009 4:46 am**

by **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.

### Re: Geometry Word Problems: The Pythagorean Theorem

Posted: **Fri Jul 17, 2009 12:22 pm**

by **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.

### Re: Geometry Word Problems: The Pythagorean Theorem

Posted: **Fri Jul 17, 2009 4:26 pm**

by **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?

Posted: **Fri Jul 17, 2009 6:23 pm**

by **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!