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ANSWERS

Solve for triangle inequalities base on the given examples.

1. Let a = 6 mm b = 12 mm and c = 5 mm. Now apply the triangle inequality theorem.

• a + b > c

• a + c > b

• b + c > a

• The given sides DO NOT make up a triangle.

2. Given the measurements: a = 4 cm, b = 11 cm. c = 13 cm. Check if the three measurements can form a triangle.

• a + b > c

• a + c > b

• b + c > a

• The three measurements can form a triangle.

3. The dimensions of a triangle are given by a = (x + 3) cm, b = (3x+7) cm and c = (4x+1) cm. Find the possible values of x that are integers.

• a + b > c

☞ the possible values of x are elements of real numbers

• a + c > b

☞ the possible values of x are numbers greater than 1.5

• b + c > a

☞ invalid, lengths can never be negative numbers

• Therefore, the possible values of x are whole numbers greater than 1.5 since we're talking about integers.

NOTE:

☞ Triangle inequality theorem suggests that the sum of any two sides of a triangle is greater than or equal to the third side of the triangle.

• a + b > c
• a + c > b
• b + c > a