Mastering Triangle Inequalities: Are You Up for the Challenge?

Question 1

Which of the following is a correct expression of the triangle inequality for sides a, b, and c?

Accepted Answer

a + b > c

Answer

a + b ≤ c

Answer

a + b = c

Answer

a + b < c

Question 2

If the lengths of two sides of a triangle are 3 cm and 7 cm, what is the maximum possible length of the third side?

Accepted Answer

9 cm

Answer

10 cm

Answer

5 cm

Answer

6 cm

Question 3

Which set of lengths can form a triangle?

Accepted Answer

6, 7, 12

Answer

2, 3, 5

Answer

3, 4, 8

Answer

5, 10, 15

Question 4

What is the minimum length of the third side if the lengths of a triangle's two sides are 8 cm and 10 cm?

Accepted Answer

3 cm

Answer

2 cm

Answer

1 cm

Answer

7 cm

Question 5

If the sides of a triangle are of lengths x, y, and z, which of the following must be true?

Accepted Answer

x + y > z and x + z > y and y + z > x

Answer

x + y < z

Answer

x + y = z

Answer

x + y ≥ z