Author’s note: In Br

i

tis

h

Englis

h, i

t’s known as

Pythagoras’ T

heorem.

the pythagorean theorem

The Pythagorean Theorem: a

2

+ b

2

= c

2

This pattern is known as The Pythagorean Theorem. Using it you

can find out whether the corner opposite the longest side of a triangle is

acute, obtuse, or a right angle. In words, the theorem is usually written:

The sum of the squares of the legs of a right

triangle is equal to the square of the hypotenuse.

T

he “h

yp

otenuse” is the

longest side.

T

hese other t

w

o

sides are ca

lled “legs.”

T

his is how it’s wri

tten as a f

ormul

a.

a

2

+ b

2

= c

2

a

c

b

a

a

2

+ b

2

> c

2

c

a

a

2

+ b

2

< c

2

For an OBTUSE triangle:

For an ACUTE triangle:

c

b

b

you are here 4 131

So we don’t need to know them

all in advance? We can check jumps

as we go? Perfect—because I’ve

just told everybody we’re setting up a

competition on one of our courses!

skate ramp magnets

Skate Ramp Magnets

Sam’s sketched out a rough design for the competition course. She wants

three different sets of ramps for the skaters to demo their skills on—one

with a gap to jump and two with joining rails to slide on.

Using the Pythagorean Theorem and the construction kit magnets, work

out where each part needs to go to complete the course design. Use each

part exactly once.

6

5

Less than 11 wide

More than 11 wide

8

Less than 11 wide

More than 11 wide

132 Chapter 3

3

6

7

8

10

4 5

the pythagorean theorem

7

I know how high I’d like them to be,

and it’d be cool if all the ramps on the

left were less than 11 wide, and all the

ramps on the right were more than 11

wide. Just use whatever you’ve got left

over for the slide rails.

3

Less than 11 wide

More than 11 wide

12

14

15

24

25

you are here 4 133

13

17

S

o

Q

t

e

u

r

r

s

t

u

g

w

gli

e

n

g

m

to g

?

et

h

s

t

a

k

rt

u

ed

?

t

F

ee

N

li

n

g

Dv

h

l

ed

C ec

o t h

e

o

u

m

b

e

i

o

n

s

o

n p

age

14

1

to get

o

f

f

t

h

e

blocks....

If y

ou don’t know y

our

square number

s make

y

our

self a list when y

ou

s

tart the ques

tion.

14 was left over

after making a

ll

the tr

iangles.

skate ramp magnets solution

Skate Ramp Magnets Solution

Sam’s sketched out a rough design for the competition course. She wants

three different sets of ramps for the skaters to demo their skills on—one

with a gap to jump and two with joining rails to slide on.

Using the Pythagorean Theorem and the construction kit magnets, work

out where each part needs to go to complete the course design. Use each

part exactly once.

Solving this problem is mostly a matter of trial and error—checking to

see where you can find lengths which fit the Pythagorean Theorem:

Longest side squared = sum of other two sides squared.

6

2

+ 8

2

= 36 + 64 = 100

10

2

= 100

5

2

+ 12

2

= 25 + 144 = 169

13

2

= 169

10

13

6

5

8

14

12

17

10

8

8

6

2

+ 8

2

= 36 + 64 = 100

10

2

= 100

8

2

+ 15

2

= 64 + 225 = 289

17

2

= 289

6

15

3

6

7

8

10

4 5

134 Chapter 3

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