T

he rop

e is fixed t

o a

is closes

t t

o the

f

loor.

the end of the

rope—the height

a v

ery ta

ll per

son

needs when

swinging.

how much rope?

A longer rope swings further and lower

The wider the gap between the platforms, the more exciting the swing

will be—but there’s a catch. The TV company doesn’t just want the

widest swing, they want the widest possible swing without people

smashing into the floor!

Safety line

The floor

4m

2m

p

oint in the c

eiling here.

Comp

eti

t

or

s

tarts her

e.

In the middle of the

swing the comp

eti

t

or

T

his is the low

es

t

saf

e height f

or

2m

140 Chapter 3

If you’r

e stuck trying t

o design the skate cour

se

on page 133, then try this t

o get y

ou started.

the pythagorean theorem

So, before we can work out

anything else, we need to

quickly find how long the

rope can safely be, right?

What’s the longest the rope can be without going below the safety line?

Q:

The Pythagorean Theorem formula (c

2

= a

2

+ b

2

) looks

like it’s for finding the hypotenuse (c). But sometimes we’re

finding a length of a short side. How do I know what I’m

supposed to be finding and how to find it?

A:You can rearrange the formula to focus on one of the short

sides (legs). Like a

2

= c

2

– b

2

or b

2

= c

2

– a

2

, but the most reliable

thing to do is to focus on the meaning behind the pattern. If you’re

looking for the hypotenuse remember that the squares of the two

shortest sides add up to make the square of the longest side.

If you’re finding a short side then you need to think of the pattern

like this: the difference between the square of the longest side and

another side is the square of the remaining side.

Q:

OK, that’s not so bad when I’m given the lengths of

two sides and I have to find the other side’s length. But what

about when I’m only given one side and I have to find integer

values that complete a right triangle? The formula can’t give

me the answer because I don’t have enough values!

A:Again, think about the pattern behind the formula. If you’ve

got a load of possible values—or if you know the value is within a

range (like “less than 20”)—then here’s a trick you can rely on to

find the answers: just remember that this pattern is about square

numbers. (1, 4, 9, 16, 25, 36, 49, 64, 81, 100,…etc).

Write down all the values you’ve been given to choose between,

and then write down their squares. Then compare pairs of

numbers and see whether they add up to a square number, or

whether the difference between them is a square number.

you are here 4 141

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