Question

Consider the following triangle side lengths and determine if the triangle could exist. Justify your answer. Part A: 21,18,17 Part B: 3,12,8

Answer 1

By applying the Triangle Inequality Theorem, we conclude that a triangle with side lengths of 21, 18, and 17 can exist because each pair of sides adds up to more than the remaining side, whereas a triangle with side lengths of 3, 12, and 8 cannot exist because one required condition is not met.

Step-by-step explanation:

To determine if a triangle with given side lengths could exist, we use the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. For Part A, with side lengths of 21, 18, and 17, we perform the following checks:

21 + 18 > 17

21 + 17 > 18

• 18 + 17 > 21

All these conditions are true, so a triangle with these side lengths can exist.

For Part B, with side lengths 3, 12, and 8, we again check:

• 3 + 12 > 8
• 3 + 8 > 12 (This is not true, 11 is not greater than 12)
• 12 + 8 > 3

Since one of the conditions is not met, a triangle with side lengths of 3, 12, and 8 cannot exist.

Answer 2

A yes, B no

Step-by-step explanation:

The triangle inequality states that the sum of any 2 sides of the triangle must be greater than the third side.

A Given 21, 18, 17 , then

21 + 18 = 39 > 17

21 + 17 = 38 > 18

18 + 17 = 35 > 21

Thus the triangle could exist

B Given 3, 12, 8 , then

3 + 12 = 9 > 8

3 + 8 = 11 < 12 ← fails the test

Thus the triangle does not exist