000RM.dvi

6.5 Dissecting a rectangle into Pythagorean triangles 217

Exercise

1.A man has a square field, 60 feet by 60 feet, with other property

adjoining the highway. He put up a straight fence in the line of 3

trees, atA,P,Q. If the distance betweenPandQis 91 feet, and

that fromPtoCis an exact number of feet, what is this distance?

60

60

91

?

A B

D C

P

Q

2.What is the least number of matches of equal lengths to make up

the following configuration?

3.What is the least number of matches of equal lengths to make up

the following configuration?

4.Do there exist Pythagorean triangles whose sides are Fibonacci

numbers?

5.Give an example of a primitive Pythagorean triangle in which the

hypotenuse is a square.

6.Give an example of a primitive Pythagorean triangle in which the

evenleg is a square.