Which lengths could be the sides of a triangle?

Any two sides must be longer than the third side, and every side must be longer than the difference of the other two sides.
A. 8+10 > 17. True
B. 12+9 < 22 False
C. 12+8 < 22 False
D. 9+8 = 17 False ← could be a degenerate triangle or a triangle with zero height, AKA straight line segment

Only the lengths described in A could be the sides of a non-degenerate triangle.

In a triangle, the sum of the two shorter sides must be greater than the longest side.

A.
(8 + 10) cm = 18 cm > 17 cm
This could be a triangle.

B.
(12 + 9) cm = 21 cm < 22 cm
This is NOT a triangle.

C.
(12 + 8) cfm = 20 cm < 22 cm
This is NOT a triangle.

D.
(8 + 9) cm = 17 cm = 17 cm
This is NOT a triangle.


The answer: A: 17 cm, 8 cm, 10 cm

A

Add the lengths of the 2 shorter legs. They must be greater than the length of the longest leg

The sum of the two smaller sides of a triangle must be more than the largest side or it can't be constructed.

The answer is A.