hwiya320 wrote:
sum of any 2 sides are GREATER than 3rd side.
yep.
this is actually an offshoot of something you probably learned sometime around first grade:
the shortest path from one point to another is a straight line (segment).
if you draw a triangle, then notice that each side of the triangle is a straight path from one vertex to another.
the other 2 sides, taken together, are a non-straight path between the same two vertices.
therefore, the other 2 sides are longer than the chosen side.
that is all.
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btw, there's another, equally useful, inequality that you should also know about triangles:
THIRD SIDE INEQUALITY
if you KNOW two sides of a triangle, then
DIFFERENCE < third side < SUM
this can be derived directly from the triangle inequality (the thing discussed above), but it's worth memorizing separately; the last thing you want to do on a 2-minute problem is start deriving new rules.
in this problem, this rule immediately yields
5 - 2 < third side < 5 + 2
3 < third side < 7
10 < perimeter < 14 (add 7 to both sides)
done.
Ron has been teaching various standardized tests for 20 years.
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