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Pythagorean theorem word problems




Pythagorean theorem word problems arise in numerous situations. We will cover a couple a solid examples here.



Pythagorean problem # 1

John leaves school to go home. He walks 6 blocks North and then 8 blocks west. How far is John from the school?

Here is how you can model this situation

East-west-north-south-image

The distance from school to home is the length of the hypotenuse.

Let c be the missing distance from school to home and a = 6 and b = 8



c2 = a2 + b2

c2 = 62 + 82

c2 = 36 + 64

c2 = 100

c = √100

c = 10

The distance from school to home is 10 blocks.

Pythagorean problem # 2

A 13 feet ladder is placed 5 feet away from a wall. The distance from the ground straight up to the top of the wall is 13 feet Will the ladder the top of the wall?

East-west-north-south-image

Let the length of the ladder represents the length of the hypotenuse or c = 13 and a = 5 the distance from the ladder to the wall.

c2 = a2 + b2

132 = 52 + b2

169 = 25 + b2

169 - 25 = 25 - 25 + b2 (minus 25 from both sides to isolate b2 )

144 = 0 + b2

144 = b2

b = √144 = 12

The ladder will never reach the top since it will only reach 12 feet high from the ground yet the top is 14 feet high.





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