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vladmire
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 Posted: Wed Dec 03, 2008 7:37 pm Post subject: Triangles |
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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. |
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hwiya320
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| Posted: Wed Dec 03, 2008 7:49 pm Post subject: Re: Triangles |
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| 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. |
sum of any 2 sides are GREATER than 3rd side.
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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lunarpower
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| Posted: Wed Dec 03, 2008 11:22 pm Post subject: Re: Triangles |
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| hwiya320 wrote: |
sum of any 2 sides are GREATER than 3rd side.
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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.
--
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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ron purewal
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