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 Write-up

Water Stopater Stop
The rectangular field pictured has unknown dimensions. Tom and Paul are both at point A. Tom walks straight from A to C. To get a drink, Paul walks from A to B, then from B to C. How far does Paul walk if he travels 40 yards farther than Tom? What are the dimensions of the field?

Problem setup

I will need to use some sort of Pythagorean Theory to solve this problem.

Plans to Solve/Investigate the Problem

The first thing I think of is to use the Pythagorean Theory.  But this problem has a twist to it.  The equation to solve is actually side A + side C = side B +40.  I think I could solve it initially with Excel.

Investigation/Exploration of the Problem

With the help of our class, I set up the following Excel:

 a c b a+c b+40 a^2 c^2 a^2+c^2 b^2 30 40 50 70 90 900 1600 2500 2500 24 32 40 56 80 576 1024 1600 1600 33 44 55 77 95 1089 1936 3025 3025 60 80 100 140 140 3600 6400 10000 10000

We stopped with the last line, because when the two yellow columns equal each other, the problem has a solution.  After we did solved for one solution, we decided we wanted to see if there were more than 1 solution.  We set up another Excel spread sheet, which is below.

 c a b 41 840 841 841 42 440 442 442 43 306.6667 309.6667 309.6667 44 240 244 244 45 200 205 205 46 173.3333 179.3333 179.3333 47 154.2857 161.2857 161.2857 48 140 148 148 49 128.8889 137.8889 137.8889 50 120 130 130 51 112.7273 123.7273 123.7273 52 106.6667 118.6667 118.6667 53 101.5385 114.5385 114.5385 54 97.14286 111.1429 111.1429 55 93.33333 108.3333 108.3333 56 90 106 106 57 87.05882 104.0588 104.0588 58 84.44444 102.4444 102.4444 59 82.10526 101.1053 101.1053 60 80 100 100 61 78.09524 99.09524 99.09524 62 76.36364 98.36364 98.36364 63 74.78261 97.78261 97.78261 64 73.33333 97.33333 97.33333 65 72 97 97 66 70.76923 96.76923 96.76923 67 69.62963 96.62963 96.62963 68 68.57143 96.57143 96.57143 69 67.58621 96.58621 96.58621 70 66.66667 96.66667 96.66667

This shows that there are multiple solutions, not just one.

Author & Contact
Meg Ramsey

Link(s) to resources, references, lesson plans, and/or other materials
Pythagorean Theory