Head First 2D Geometry

you are here 4 121

the pythagorean theorem

Any good jump has some similar scaled cousins

Use factor trees to find whole-number miniatures

Factor Tree Factor Tree Factor Tree

10 8 6

222 345

Each of these

rows contains

the number

2, so that's a

common factor.

All the lengths are

HALF the size of

the 10-8-6 ramp.

The other

numbers tell

you what the

lengths of sides

on your scaled

ramp will be.

What’s the next largest ramp you can build that is similar to the

10-8-6 design?

5

4

3

When you scale the ramp—making it bigger or smaller—none

of the angles change, so it stays a good ramp with a right angle.

To find whole number lengths for the smaller-scaled sizes, look

for a common factor in your current lengths. That’s easiest to do

by using a set of factor trees.

10

8

6

10 = 2 x 5

122 Chapter 3

sharpen solution

What’s the next largest ramp you can build that is similar to the

10-8-6 design?

The lengths 15, 12, and 9 have the same ratios as

10-8-6 and as 5-4-3.

5 x 3 = 15

4 x 3 = 12

3 x 3 = 9

10 x 1.5 = 15

8 x 1.5 = 12

6 x 1.5 = 9

It doesn’t matter whether you

used the original ramp or the

mini version to do your scaling—

it works out just the same!

Q:

What if I wanted a ramp even smaller? Can I just keep

doing more factor trees?

A: The Kwik-klik units don’t come in half sizes—there isn’t a 1.5

length, so you’d ...