Pythagorean Theorem

Problems

Solved


1. Staring with the picture at tthe right we have the hypotenuse equal to and one of the legs is equal to . The Pythagorean Theorem states that the square of the hypotenuse is equal to the sum of the squares of the legs. or:

Since MN is a length, we only need the positive square root. Recall the geometric mean definition: the geometric mean of two positive numbers a,b is . Therefore MN is the geometric mean of a and b.

 

  2. 3. 4. 5. 6. 7. 8. 9.
 a  3

6

 5

 8

11 3n

6
 b 44 8

12

15

60

4n  
 c

 5

10 13 17 61

5n

6

 12

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