Question

Determine if the side lengths could form a triangle. Use an inequality to prove your answer.



a) 16 m, 21 m, 39 m



b) 34 km, 27 km, 58 km



c) 29 ft, 38 ft, 9 ft

Answer 1

9514 1404 393

Answer:

  a) no

  b) yes

  c) maybe (no)

Step-by-step explanation:

There are two versions of the triangle inequality. One requires ...

  a + b > c

for any triple of side measures a, b, c.

The other allows ...

  a + b ≥ c

which admits "triangles" that have zero height and look like line segments.

Most questions asking "do these lengths form a triangle" are concerned with the "greater than" case, and disallow the "or equal to" case.

__

a)

  $16+21=37\ngtr39\qquad\text{not a triangle}$

b)

  $27+34=61>58\qquad\text{could be a triangle}$

c)

  $9+29=38\ge38\qquad\text{could be a triangle if "equal to" is allowed}$