Finding an Unknown Side - Set 1 PT 1 - Math Antics

?

Name:

Date:

Finding an Unknown Side - Set 1

Instructions: For each right triangle, use the Pythagorean Theorem to find the length of the unknown side `x'. (You can use a calcuator for the arithmetic if you want to.)

PT 1

1 x

4

2

x

15

4

42 + 42 = x2 16 + 16 = x2

32 = x 2

x2 = 32

x = 32

or 4 2 or 5.656...

12

x2 + 122 = 152 x2 + 144 = 225

-144 -144 x2 = 81

x2 = 81 x=9

3

13

x

4 x

6

3

x2 + 32 =

2

13

x2 + 9 = 13

-9 -9

x2 = 4

x2 = 4 x=2

2

6 2+ 22 = x2 6 + 4 = x2

10 = x2

x2 = 10 x = 10 or 3.162...

5 4

x

3

x2 + 32 = 42 x2 + 9 = 16

-9 -9 x2 = 7

x2 = 7 x= 7 or 2.645...

The Pythagorean Theorem ?

6 2.5 1.5

x

x2 + 1.5 2 = 2.52 x2 + 2.25 = 6.25

-2.25 -2.25 x2 = 4

x2 = 4 x=2

? 2017 Math Plus Motion, LLC

?

Name:

Date:

Finding an Unknown Side - Set 2

Instructions: For each right triangle, use the Pythagorean Theorem to find the length of the unknown side `x'. (You can use a calcuator for the arithmetic if you want to.)

PT 2

1 x

6

8

62 + 82 = x2 36 + 64 = x2

100 = x2

x2 = 100 x = 10

2

26

x

x2 + 12 =

2

26

x2 + 1 = 26

-1 -1

x2 = 25

1

x2 = 25 x=5

3 x

3

6 2+ 32 = x2 6 + 9 = x2

15 = x2

6

x2 = 15 x = 15 or 3.872...

4

50

5

x

2

5

+

x2 =

50 2

25 + x2 = 50

-25

-25

x2 = 25

x2 = 25 x=5

5

x

12

2

x2 + 22 = 12 2 x2 + 4 = 12

-4 -4

x2 = 8

x2 = 8

x= 8 or 2 2 or 2.828...

The Pythagorean Theorem ?

6 x 0.3

0.4

0.32 + 0.42 = x2 0.09 + 0.16 = x2

0.25 = x2

x2 = 0.25 x = 0.5 or 0.25

? 2017 Math Plus Motion, LLC

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Date:

Is it a right triangle?

Instructions: Use the Pythagorean Theorem to test the triangles shown or described in each problem below.

PT 3

1 If a triangle has sides that are 12, 10 and 6 meters long, is it a right triangle?

NOTE: when plugging the three sides into the test equation, always make the longest side `c'.

Test: 62 + 102 =? 122 36 + 100 =? 144

136 = 144 Nope!

2 Is this a right triangle?

32

4

Test:

4

42 + 42 =?

2

32

16 + 16

?

=

32

32 = 32 Yes

3 Is a triangle with side lengths of 4, 5, and 6 inches a right triangle?

Test:

42 +

52

?

=

62

16 + 25

?

=

36

41 = 36 No

4 A triangle has side lengths that are 7 cm, 7 cm and 11cm. Is it a right triangle ?

Test:

72 +

72

?

=

112

49 + 49

?

= 121

98 = 121 No

5 Is this a right triangle? 41

5 4

Test:

42 + 52 =?

2

41

16 + 25 =? 41

41 = 41 Yes

6 Is this a right triangle?

5

3

13

Test:

32 +

5 2 =?

2

13

9 + 5 =? 13

14 = 13 No

The Pythagorean Theorem ?

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