## dariyana 3 years ago A triangle has the following measurements. What is a possible length for the third side? AB = 5, BC = 7, CA = ? 2 12 5 13

1. dariyana

@Wired

2. dariyana

i think it B

3. lgbasallote

*greater

4. Wired

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

5. Wired

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

6. dariyana

so it would be 13

7. eyust707

|dw:1341624363071:dw|

8. eyust707

i dont think 13 will work

9. eyust707

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

10. dariyana

when you add the two they equal 12

11. eyust707

Yes so it cant be 12 either

12. eyust707

other wise they would be flat on top of each other

13. Wired

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.

14. eyust707

12 doesnt work: |dw:1341624504291:dw|

15. dariyana

lol so it 5

16. eyust707

YEP! its 5 Cause 2 is too small |dw:1341624584353:dw|

17. Calcmathlete

Here. x < 5 + 7 x + 5 > 7 x < 12 x > 2 Therefore, you know that the set of numbers possible are \(2 < x < 12\). Which of those numbers is within that range?

18. dariyana

ok thanks you guys

19. Calcmathlete

You're welcome :)