Section 9.6 The Pythagorean Theorem
971
Version: Fall 2007
9.6
Exercises
In
Exercises 1

8
, state whether or not
the given triple is a Pythagorean Triple.
Give a reason for your answer.
1.
(8
,
15
,
17)
2.
(7
,
24
,
25)
3.
(8
,
9
,
17)
4.
(4
,
9
,
13)
5.
(12
,
35
,
37)
6.
(12
,
17
,
29)
7.
(11
,
17
,
28)
8.
(11
,
60
,
61)
In
Exercises 9

16
, set up an equation
to model the problem constraints and solve.
Use your answer to ﬁnd the missing side
of the given right triangle.
Include a
sketch with your solution and check your
result.
9.
2
√
3
2
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1
10.
2
2
11.
4
8
12.
10
12
13.
2
2
√
3
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Chapter 9 Radical Functions
Version: Fall 2007
14.
12
4
√
3
15.
5
10
16.
8
√
2
8
In
Exercises 17

20
, set up an equation
that models the problem constraints. Solve
the equation and use the result to answer
the question. Look back and check your
result.
17.
The legs of a right triangle are con
secutive positive integers. The hypotenuse
has length 5. What are the lengths of the
legs?
18.
The legs of a right triangle are con
secutive even integers. The hypotenuse
has length 10. What are the lengths of
the legs?
19.
One leg of a right triangle is 1 cen
timeter less than twice the length of the
ﬁrst leg. If the length of the hypotenuse
is 17 centimeters, ﬁnd the lengths of the
legs.
20.
One leg of a right triangle is 3 feet
longer than 3 times the length of the ﬁrst
leg. The length of the hypotenuse is 25
feet. Find the lengths of the legs.
21.
Pythagoras is credited with the fol
lowing formulae that can be used to gen
erate Pythagorean Triples.
a
=
m
b
=
m
2
−
1
2
,
c
=
m
2
+ 1
2
Use the technique of Example 6 to demon
strate that the formulae given above will
generate Pythagorean Triples, provided
that
m
is an
odd
positive integer larger
than one.
Secondly, generate at least
3 instances of Pythagorean Triples with
Pythagoras’s formula.
22.
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 Pythagorean Theorem, Right triangle, pythagorean triples, problem constraints, Approximate your answer

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