Final Assignment Problem 4 (from set 6 exercise 4)

At this point we have the Pythagorean theorem ( where a and b are legs in a right triangle and c is the hypotenuse).

(a) Illustrate the meaning of .

(b) Now I’ll illustrate 7sqrt(3):

(c) Illustrate (2/3)sqrt(5):

At this point it is clear that we just need to dilate sqrt(5) by 2/1 and 1/3.

(d) We can now see that a(sqrt(3)) must mean sqrt(3) dilated by a/1, sqrt(3)/b must mean sqrt(3) dilated by 1/b, and (a/b)sqrt(3)

must be sqrt(3) dilated by a/1 and 1/b.

(e) If we are given a segment of length (3/5)sqrt(a) then dilating by 3/1 and 1/5 will give us sqrt(a).