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 |