# CLASSIFYING TRIANGLES USING PYTHAGOREAN THEOREM WORKSHEET

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.

State if the three side lengths form an acute, obtuse, or right triangle.

Problem 1 :

5, 12, 13

Solution:

Let a = 5, b = 12 and c = 13

c2 ? a2 + b2

13² ? 5² + 12²

169 ? 25 + 144

169 = 169

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

Problem 2 :

4, 12, 13

Solution:

Let a = 4, b = 12 and c = 13

c2 ? a2 + b2

13² ? 4² + 12²

169 ? 16 + 144

169 > 160

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

Problem 3 :

9, 12, 15

Solution:

Let a = 9, b = 12 and c = 15

c2 ? a2 + b2

152 ? 92 + 122

225 ? 81 + 144

225 = 225

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

Problem 4 :

3, 4, 5

Solution:

Let a = 3, b = 4 and c = 5

c2 ? a2 + b2

52 ? 32 + 42

25 ? 9 + 16

25 = 25

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

Problem 5 :

9, 2√22, 13

Solution:

Let a = 9, b = 2√22 and c = 13

c2 ? a2 + b2

132 ? 92 + (2√22)2

169 ? 81 + 88

169 = 169

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

Problem 6 :

√7, √11, 4

Solution:

Let a = √7, b = √11 and c = 4

c2 ? a2 + b2

42 ? √72 +√112

16 ? 7 + 11

16 < 18

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

Problem 7 :

14, 5√7, 16

Solution:

Let a = 14, b = 5√7 and c = 16

c2 ? a2 + b2

162 ? 142 + (5√7)2

256 ? 196 + 175

256 < 371

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

Problem 8 :

√11, √10, √21

Solution:

Let a = √11, b = √10 and c = √21

c2 ? a2 + b2

√212 ? √112 + √102

21 11 + 10

21 = 21

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

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