The triangle inequality theorem will come into play here. The basic idea of this theorem is "take any two sides of a triangle and add them up. That sum must be larger than the third side".
So if we have a = 12 b = x c = 15
then the following must hold true (all three inequalities must be true) a+b > c a+c > b b+c > a
Focus on the first inequality and plug in the given values. Then solve for x a+b > c 12+x > 15 12+x-12 > 15-12 x > 3
So we see that x > 3. Repeat the same for the second inequality a+c > b 12+15 > x 27 > x x < 27
Repeat again for the third inequality b+c > a x+15 > 12 x+15-15 > 12-15 x > -3
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In summary so far, we have x > 3 x < 27 x > -3
Combine all of those inequalities to form one single compound inequality which is 3 < x < 27
For some reason your teacher doesn't want you to focus on the "less than 27" part, so it seems like s/he only wants the "x > 3" portion.
So this is why x must be larger than 3 (up only til you get to 27 though).
when rounding numbers: if it's four or less, you round down. if it's five or more, you round up. 9 is bigger than 4, so the nearest whole number is 830.
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