A triangle has the following measurements. What is a possible length for the third side?
AB = 5, BC = 7, CA = ?
Stacey Warren - Expert brainly.com
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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
If they were less than or equal to the third side, you wouldn't have a triangle.
so it would be 13
i dont think 13 will work
We could make them all the way flat but they still wouldnt be 13
when you add the two they equal 12
Yes so it cant be 12 either
other wise they would be flat on top of each other
AB + BC > CA
7 + 5 > CA
12 > CA
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.
12 doesnt work:
lol so it 5
YEP! its 5
Cause 2 is too small
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?