Question

By the Triangle Inequality Theorem which set of side lengths could create a triangle? A) 5, 10, 4 B) 5, 7, 13 C) 7, 9, 3 D) 10, 4, 5

Answer 1

The correct answer is C.

Triangle inequality means 2 sides of the triangle added up must be longer than the remaining side. Therefore, to find the correct answer quickly, we can add up the shortest 2 sides and see if they exceed the remaining side.

For A,
5 + 4 = 9
9 < 10
Therefore, A is incorrect.

For B,
5 + 7 = 12
12 < 13
Therefore, B is not correct.

For C,
7 + 3 = 10
10 > 9
C is the correct answer.

Heres D, to make sure the answer C is correct.
4 + 5 = 9
9 < 10
D is not correct.

Let's add up the remaining sides to make sure C completely satisfies the rule.

9 + 3 = 12
12 > 7
7 + 9 = 16
16 > 3

Therefore, the answer is C.