# CONVERSE OF THE PYTHAGOREAN THEOREM FOR CLASSIFYING TRIANGLE

Let a, b and c be the sides of the triangle.

• If a2 + b2 > c2, the triangle is acute triangle.
• If a2 + b2 = c2, the triangle is right triangle.
• If a2 + b2 < c2, the triangle is obtuse triangle.

Where a and b are the lengths of the two shorter sides and c be the length of the longest side.

Classify the triangle as acute, right, or obtuse, explain.

Problem 1 :

Solution:

Let c represent the length of the longest side of the triangle.

c2 ? a2 + b2

62 ? 52 + 22

36 ? 25 + 4

36 > 29

Because c2 is greater than a2 + b2, the triangle is obtuse.

Problem 2 :

Solution:

Let c represent the length of the longest side of the triangle.

c? a2 + b2

172 ? 82 + 152

289 ? 64 + 225

289 = 289

Because c2 is equal to a2 + b2, the triangle is right.

Problem 3 :

Solution:

Let c represent the length of the longest side of the triangle.

c? a2 + b2

72 ? 72 + 72

49 ? 49 + 49

49 < 98

Because c2 is less than a2 + b2, the triangle is acute.

Use the side lengths to classify the triangle as acute, right, or obtuse.

Problem 4 :

7, 24, 24

Solution:

By Triangle Inequality Theorem, the above set of numbers can represent the side lengths of a triangle.

Compare the square of the length of the longest side with the sum of the squares of the lengths of the two shorter sides.

c2 ? a2 + b2

24272 + 242

576 49 + 576

576 < 625

Because c2 is less than a2 + b2, the triangle is acute.

Problem 6 :

7, 24, 25

Solution:

By Triangle Inequality Theorem, the above set of numbers can represent the side lengths of a triangle.

Compare the square of the length of the longest side with the sum of the squares of the lengths of the two shorter sides.

c2 ? a2 + b2

252 72 + 242

625 ? 49 + 576

625 = 625

Because c2 is equal to a2 + b2, the triangle is right.

Problem 7 :

7, 24, 26

Solution:

By Triangle Inequality Theorem, the above set of numbers can represent the side lengths of a triangle.

Compare the square of the length of the longest side with the sum of the squares of the lengths of the two shorter sides.

c2 ? a2 + b2

262 72 + 242

676 ? 49 + 576

676 > 625

Because c2 is greater than a2 + b2, the triangle is obtuse.

Determine whether the triangle is acute, right, or obtuse.

Problem 8 :

Solution:

Let c represent the length of the longest side of the triangle.

c2 ? a2 + b2

52 ? 42 + 42

25 ? 16 + 16

25 < 32

Because c2 is less than a2 + b2, the triangle is acute.

Problem 9 :

Solution:

Let c represent the length of the longest side of the triangle.

c2 ? a2 + b2

142 ? 122 + 62

196 144 + 36

196 > 180

Because c2 is greater than a2 + b2, the triangle is obtuse.

Problem 10 :

Solution :

Let c represent the length of the longest side of the triangle.

c2 ? a2 + b2

152 ? 122 + 92

225 144 + 81

225 = 225

Because c2 is equal to a2 + b2, the triangle is right.

Problem 11 :

Match the side lengths of a triangle with the best description.

 1) 2, 10, 112) 8, 5, 73) 5, 5, 54) 6, 8, 10 A. rightB. acuteC. obtuseD. equiangular

Solution:

1) By Pythagorean Theorem,

112 = 22 + 10

121 = 4 + 100

121 > 104

It is obtuse triangle.

2) By Pythagorean Theorem,

72 = 82 + 52

49 = 64 + 25

49 < 89

It is acute triangle.

3)

5, 5, 5

It is equiangular triangle.

4) By Pythagorean Theorem,

102 = 62 + 82

100 = 36 + 64

100 = 100

It is right triangle.

 1) 2, 10, 112) 8, 5, 73) 5, 5, 54) 6, 8, 10 C. obtuseB. acuteD. equiangularA. right

## Recent Articles

1. ### Finding Range of Values Inequality Problems

May 21, 24 08:51 PM

Finding Range of Values Inequality Problems

2. ### Solving Two Step Inequality Word Problems

May 21, 24 08:51 AM

Solving Two Step Inequality Word Problems