The sum of the 2 shortest sides of any triangle cannot be greater than the longest side correct? This is how I came up with none for this problem correct?
If two sides of a triangle have lengths 2 and 5, which of the following could be the perimeter of the triangle?
a.9
b.15
c.19
none.
Triangles
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sum of any 2 sides are GREATER than 3rd side.vladmire wrote:The sum of the 2 shortest sides of any triangle cannot be greater than the longest side correct? This is how I came up with none for this problem correct?
If two sides of a triangle have lengths 2 and 5, which of the following could be the perimeter of the triangle?
a.9
b.15
c.19
none.
a. 9-7= 2
b. 15-7 = 8
c. 19-7 = 11
I would pick none, but for sum of 2 > 3rd
think of 3-4-5 right triangle. by your logic, 3+4 has to be less than 5... so does that mean right triangle is not a real triangle?
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yep.hwiya320 wrote: sum of any 2 sides are GREATER than 3rd side.
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.
--
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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yeah.Andrei wrote:Thanks lunarpower, I knew the 1st rule but forgot about the second!
THIRD SIDE INEQUALITY
if you KNOW two sides of a triangle, then
DIFFERENCE < third side < SUM
some books don't mention both of them, since the second rule (the one with sum/difference) can be derived directly from the first one.
however, since time pressure is so intense on the gmat, it's better to just have them both memorized.
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why did u add 7 in both sides?lunarpower wrote:yep.hwiya320 wrote: sum of any 2 sides are GREATER than 3rd side.
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.
--
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.
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3 < third side < 7 is just the range of values for the third side of the triangle.mbr10525 wrote:why did u add 7 in both sides?
you're looking for the range of values for the whole perimeter, so you have to add the lengths of the other two sides. these sides are 2 and 5, for a total of 7 that you have to add to achieve the whole perimeter.
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Quand on se sent bien dans un vêtement, tout peut arriver. Un bon vêtement, c'est un passeport pour le bonheur.
Yves Saint-Laurent
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