Question

A triangle has two sides of lengths 6 and 9

the third side be?
Check all that
What value
apply.
could the length of

Answer 1

A, C, E, F

Explanation:

since nothing else was said, it is a general triangle. nothing special about it.

so, the only rules are that the sum of any pair of sides must be longer than the 3rd side (otherwise, if the 3rd side is longer, the sides could not connect).

A. 10.

so, we have

6 + 9 > 10 true

6 + 10 > 9 true

9 + 10 > 6 true

therefore this is a possible 3rd side.

B. 2.

so, we have

6 + 9 > 2 true

6 + 2 > 9 false

9 + 2 > 6 true

therefore this is NOT a possible 3rd side.

C. 4.

so, we have

6 + 9 > 4 true

6 + 4 > 9 true

9 + 4 > 6 true

therefore this is a possible 3rd side.

D. 15.

so, we have

6 + 9 > 15 false

6 + 15 > 9 true

9 + 15 > 6 true

therefore this is NOT a possible 3rd side (this triangle is a special case as 6+9 = 15 : it can only exist as a completely flat line and is therefore not a triangle).

E. 12.

so, we have

6 + 9 > 12 true

6 + 12 > 9 true

9 + 12 > 6 true

therefore this is a possible 3rd side.

F. 7.

so, we have

6 + 9 > 7 true

6 + 7 > 9 true

9 + 7 > 6 true

therefore this is a possible 3rd side.