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13.01 Pythagoras' theorem

Worksheet
Pythagorean triples
1

Determine whether the following are Pythagorean triples:

a
\left(3, 4, 5\right)
b
\left(12, 5, 13\right)
c
\left(8, 13, 19\right)
d
\left(9, 16, 25\right)
e
\left(6, 8, 10\right)
f
\left(300, 400, 500\right)
g
\left(6, 8, 10\right)
h
\left(\dfrac{1}{3}, \dfrac{1}{4}, \dfrac{1}{5}\right)
2

If x, y, and z form a Pythagorean triple, will 3 x, 3 y and 3 z be a Pythagorean triple? Explain your answer.

Right-angled triangles
3

Name the hypotenuse of each triangle:

a
b
c
4

Use Pythagoras' theorem to determine whether the following are right-angled triangles:

a
b
5

Determine whether the following represent the sides of a right-angled triangle:

a
\left(6, 8, 13\right)
b
\left(3, 4, 5\right)
c
\left(2, 4, 6\right)
d
\left(5, 12, 13\right)
6

Consider the following right-angled triangle:

Write an equation that can be constructed from the given information.

7

Given that the length of the hypotenuse of a right-angled triangle is 20, find the two other side lengths that would complete a Pythagorean triple.

8

A right-angled triangle has side lengths x, y, and hypotenuse z. Will a triangle with side lengths of 2 x, 2 y and 2 z make a right-angled triangle as well? Explain your answer.

9

Consider the right-angled triangle with sides \left(7, 24, 25\right).

a

What is the length of the side that is opposite the largest angle?

b

Find the lengths of the two sides that are next to the right angle.

Applications
10

Three towns Melba, Florey and Giralang are positioned as shown in the diagram:

Which two towns are furthest apart, assuming a direct route is taken?

11

A group of engineering students have made a triangle out of some wooden strips. They have made a triangle with sides lengths 20, 48, and 52 \text{ m}.

a

Is the triangle they make a right-angled triangle?

b

How many metres of wooden strips did they use to make the triangle?

c

Determine whether the following right-angled triangles can be created using the exact same length of wooden strips:

i
\left(30, 40, 50\right)
ii
\left(26, 41, 53\right)
iii
\left(14, 48, 50\right)
iv
\left(24, 45, 51\right)
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Outcomes

MA4-16MG

applies Pythagoras' theorem to calculate side lengths in right-angled triangles, and solves related problems

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