Question

Which of the side lengths could form a triangle?
A) 2 cm, 2 cm, 4 cm
B) 3 cm, 5 cm, 10 cm
C) 3 cm, 4 cm, 5 cm
D) 4 cm, 8 cm, 15 cm

( help?!)

Answer 1

Do you know about the triangle inequality statement? That would be very useful here.

Answer 2

no i have not

Answer 3

The essential statement is that, these three sides need to be the right lengths so that they do not deform into a segment or worse yet, into an opened three segments. Like this:


So what we want to do is, check the side lengths a, b, and c for three cases:
a + b > c b + c > a, and a + c > b
For an example, here is (A) evaluated:
a=2 cm, b = 2cm, and c = 4 cm;
2 + 2 > 4
4 > 4 4 is equal to 4, so this is NOT true! So, (A) does not represent a triangle! It is a line segment.
Although: 4 + 2 > 2 and 4+ 2 > 2 do work out, but for triangle inequality to be satisfied we have to have ALL THREE as true!

Answer 4

So to proceed, we just test this same thing for (B), (C), and (D) until we find one that works. Does this all seem clear?

Answer 5

yes . . . would it be C.

Answer 6

(C) looks good!
3 + 4 > 5
7 > 5 checks out.
3 + 5 > 4 is clearly true, and
4 + 5 > 3 is also clearly true. Good work!

Answer 7

Alright thanks. Your a big help!. :)

Answer 8

You're welcome! :D