Title
Water Stop
Problem Statement
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
The problem wants us to find
the length of two sides of a rectangle, specifically sides AB and AC.
Plans to
Solve/Investigate the Problem
My initial plan was to substitute
values in for the different dimensions to guess what the dimensions were;
making sure that the distance from AB to BC is 40 units greater than the
distance from AC.
Investigation/Exploration
of the Problem
In order to substitute values
in for the different dimensions, I decided to use an Excel Spreadsheet to
manipulate the numbers like the one below. I used the Pythagorean Theorem in
order to determine the relationship of the sides. Based on the 345 triple, I used
multiples of this triple to determine my values.
a

c

b

a+c

b+40

a^2+b^2

c^2

30

40

50

70

90

2500

2500

40

40

56.569

80

96.569

3200

3200

24

32

40

56

80

1600

1600

60

80

100

140

140

10000

10000

24.5

32.3

40.541

56.8

80.541

1643.54

1643.5

From the spreadsheet, I looked
at the numbers that fit the terms of the solution. The column marked with “a+c” had to be the same as the column marked with
“b+40” in order to satisfy the terms of the solution.
Extensions of the Problem
As we worked through the
problem, we found multiple solutions that fit the terms of the
solution. Our goal was to try
to find an algebraic equation that determined the other solutions. We set
up an equation (a+c40)²=b², and solved for a. We came up with the formula
40c800/c40=a. Another
spreadsheet was then created using the formula as our guide. The spreadsheet confirmed the fact
that there were multiple solutions.
Author & Contact
Mesha Rainey
Email Ms. Rainey
Link(s) to resources, references, lesson plans, and/or other
materials
Pythagorean
Theorem
U
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