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 Write-up

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

This problem is asking you to find the dimensions of the triangle formed given the distances that Tom and Paul walked.

Plans to Solve/Investigate the Problem

My initial plans were to use the Pythagorean Theorem in order to come up with some kind of a relationship.

Investigation/Exploration of the Problem

I initially tried to solve for some of the variables in the equation.  However, I was not able to do this because it was mathematically impossible to solve for anyone of them.  It was however possible to come up with an equation that would help to come up with numbers that would give solutions to the problem.  We decided to label segment AB – c, BC – a, and AC –b.  Based on the information given in the problem and the variables we assigned the segments, the formula c + a = 40 + b was made.  After many different calculations and taking into account the Pythagorean Theorem, we were able to come up with an equation for a,  a=.  Based on this information we were able to create an excel spreadsheet that list the different quantities that solve the problem.

Here is a portion of it.  All of these numbers for c, a, and b satisfy the problem.

 c a b c-a-40 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

Because the answer is dependent upon the variables this is a dependent system and therefore there are an infinite amount of answers.

Author & Contact
Benjamin Moore
My Email