Ask a New Question
Menu

The Triangle Inequality Theorem states that the sum of any two sides of a triangle must be greater than the measure of the third side.

a + b > c

Using this theorem, tell whether the examples below are possible triangles by selecting yes or no.

(4 points)
Yes No
a = 3, b = 2, c = 4

a = 7, b = 10, c = 18

a = 2, b = 4, c = 7

a = 5, b = 4, c = 7

Skip to navigation

1 answer

To determine whether the given sets of sides can form a triangle, we apply the Triangle Inequality Theorem, which states that for any triangle with sides a, b, and c:

  1. a + b > c
  2. a + c > b
  3. b + c > a

We will evaluate each set of values accordingly.

  1. (a = 3, b = 2, c = 4)

    • 3 + 2 > 4 (5 > 4) → True
    • 3 + 4 > 2 (7 > 2) → True
    • 2 + 4 > 3 (6 > 3) → True
    • Answer: Yes

  2. (a = 7, b = 10, c = 18)

    • 7 + 10 > 18 (17 > 18) → False
    • Since one condition is false, the triangle cannot be formed.
    • Answer: No

  3. (a = 2, b = 4, c = 7)

    • 2 + 4 > 7 (6 > 7) → False
    • Since one condition is false, the triangle cannot be formed.
    • Answer: No

  4. (a = 5, b = 4, c = 7)

    • 5 + 4 > 7 (9 > 7) → True
    • 5 + 7 > 4 (12 > 4) → True
    • 4 + 7 > 5 (11 > 5) → True
    • Answer: Yes

Final answers:

  • a = 3, b = 2, c = 4: Yes
  • a = 7, b = 10, c = 18: No
  • a = 2, b = 4, c = 7: No
  • a = 5, b = 4, c = 7: Yes