Question

A triangle has the following measurements. What is a possible length for the third side?

AB = 5, BC = 7, CA = ?

2

12

5

13

Answer 1

@Wired

Answer 2

i think it B

Answer 3

*greater

Answer 4

Thanks @lgbasallote , brain fart :)

Any two sides when added have to be greater than the third side.

Therefore, AB + BC > CA

If it was B then AB + AC = CA

Answer 5

If they were less than or equal to the third side, you wouldn't have a triangle.

Answer 6

so it would be 13

Answer 7

i dont think 13 will work

Answer 8

We could make them all the way flat but they still wouldnt be 13

Answer 9

when you add the two they equal 12

Answer 10

Yes so it cant be 12 either

Answer 11

other wise they would be flat on top of each other

Answer 12

No.
AB + BC > CA
7 + 5 > CA
12 > CA

Possible equations:
12 > 2
12 > 5
12 > 12
12 > 13

It's not 12 or 13, because 12 isn't greater than itself, and 12 isn't greater than a large number. Now, since CA = 2 or 5:

AB < BC + CA (again, two sides added up are greater than the third)

7 < 5 + 2
7 < 7

7 < 5 + 5
7 < 10

7 can't be less than itself. 7 is less than 10, so you know 5 is the answer.

Answer 13

12 doesnt work:

Answer 14

lol so it 5

Answer 15

YEP! its 5

Cause 2 is too small