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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

garamsey46@earthlink.net

Link(s) to resources, references, lesson plans, and/or other materials
Pythagorean Theory
Link 2

 

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