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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 3-4-5 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+c-40)²=b², and solved for a.  We came up with the formula 40c-800/c-40=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
E-mail Ms. Rainey

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

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