be the rope swing solution
BE the Rope Swing Solution
Your job is to play like you’re the 6m
rope. Use the Pythagorean Theorem to
work out how far across a gap someone
could swing on you.
6m
6m
X X
4m
Total distance you can swing = 2X = 2 x 4.47 = 8.94 meters
Using the Pythagorean
Thereom:
6
2
= 4
2
+ X
2
36 = 16 + X
2
36 - 16 = X
2
20 = X
2
20 = X
4.47 = X
Q:
Wait a second—weren’t we looking
for integer solutions? How come 8.94
meters is OK?
A:The Kwik-klik parts only came in
integer lengths, so we needed integer
solutions for our ramps, but for the rope
swing a non-integer solution is fine. We
can put the blocks 8 meters and 94
centimeters apart.
Q:
Right. So, generally, is this
Pythagorean thing for finding integer
solutions or not?
A:You’ll find that a lot of geometry
problems center around the “Pythagorean
triples.” You can think of them as Super
Triangles—right triangles with integer side
lengths. You’ve already found some—3,4,5
and 5,12,13 are two of the most important.
Q:
Super Triangles…cool! Do I need
to learn the actual values or just know
that they exist?
A:You can always use the Pythagorean
Theorem to find them, but that’s gonna
be pretty slow…so if you’re good at
remembering stuff then learning the first
three or four (in the toolbox at the end of
this chapter) can be a real time saver.
146 Chapter 3