CLASSIFYING TRIANGLES USING PYTHAGOREAN THEOREM WORKSHEET

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.