# CLASSIFYING TRIANGLES BY SIDES LENGTHS ACUTE OBTUSE OR RIGHT

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 each triangle is acute, obtuse, or right.

Problem 1 :

Solution:

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

c2 ? a2 + b2

162 ? 92 + 122

256 ? 81 + 144

256 > 225

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.

c2 ? a2 + b2

152 ? 92 + 92

225 ? 81 + 81

225 > 162

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

Problem 3 :

Solution:

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

c2 ? a2 + b2

102 ? 62 + 82

100 ? 36 + 64

100 = 100

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

Problem 4 :

Solution:

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

c? a2 + b2

172 ? 122 + 92

289 ? 144 + 81

289 > 225

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

Problem 5 :

Solution:

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

c? a2 + b2

152 ? 122 + (2√14)2

225 ? 144 + 56

225 > 200

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

Problem 6 :

Solution:

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

c2 ? a2 + b2

(√257)2 ? 142 + (√61)2

257 ? 196 + 61

257 = 257

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

Problem 7 :

Solution:

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

c? a2 + b2

(2√29)2 ? 42 + 102

116 ? 16 + 100

116 = 116

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

Problem 8 :

Solution:

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

c2 ? a2 + b2

(√13)2 ? (√5)2 + (2√2)2

13 ? 5 + 8

13 = 13

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

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