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PS: Geometry

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PS: Geometry [#permalink]

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New post 29 Nov 2008, 06:09
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If a triangle has sides 8, 10, and z, which of the following cannot be the area of the triangle?

(A) 3
(B) 6
(C) 12
(D) 24
(E) 46


would you please explain a fast method to solve this problem? this can be time consuming if you want to start experimenting with different combination.

thanks

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Re: PS: Geometry [#permalink]

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New post 29 Nov 2008, 06:49
Answer is A

easy method tht striked my mind is the triangle rule,

a+b > c and a-b <c

So by the above rule, 2<z<18 --- 1)

So the area cannot be 3. since z has to be multiplied with 8/2 -- 4 or 10/2 -- 5

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Re: PS: Geometry [#permalink]

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New post 29 Nov 2008, 06:58
E

sum of two sides of the triangle must be more than a value of third side, so z<18. If z=16, perimetr (p) = 34. By Heron's formula, where s=p/2, Area=sqrt ( s(s-a)(s-b)(s-c) ) = sqrt (17 (9 x 7 x 1)) = sqrt 1008 = approx.32, almost the max. possible area of this triangle, and we can conclude that answer E (46) is impossible to be the one. This is not a perfect explanation, but I can't find the shortest way to solve this problem. :roll:

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Re: PS: Geometry [#permalink]

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New post 29 Nov 2008, 08:41
the max area of a triangle is that of a Right ANGLE triangle...

so lets see the max area of the triangle 3:4:5 so you have 6:8:10

so the max area would be 1/2 *6*8=24..so the max area possible is 24..which means E is not a possible area.

I am going with E

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Re: PS: Geometry [#permalink]

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New post 29 Nov 2008, 11:06
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tarek99 wrote:
If a triangle has sides 8, 10, and z, which of the following cannot be the area of the triangle?

(A) 3
(B) 6
(C) 12
(D) 24
(E) 46


would you please explain a fast method to solve this problem? this can be time consuming if you want to start experimenting with different combination.

thanks


The max. possible area of this triangle is 1/2(8x10) = 40 if these two sides are base and perpendicular. Therefore 46 cannot be the area

The third side is greater than 2 but smaller than 18.
The area is determined by height not by the third side.
Hight could vary from 0 to 10.
More precisely 0 < height <= 10.
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GT

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Re: PS: Geometry [#permalink]

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New post 29 Nov 2008, 12:39
fresinha12 wrote:
the max area of a triangle is that of a Right ANGLE triangle...

so lets see the max area of the triangle 3:4:5 so you have 6:8:10

so the max area would be 1/2 *6*8=24..so the max area possible is 24..which means E is not a possible area.

I am going with E


wow, I LOVE your explanation! Thank you so much, and thank you everyone for the great contribution. OA is E.

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Re: PS: Geometry [#permalink]

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New post 30 Nov 2008, 10:20
There's seems to be different theories that's getting to the right answer, E, which is a good thing.

But then these different theories do not agree on what is the max area of a triangle. That is not good.

I saw the max area as either 32 vs 24 vs 40.

Then there's selvae's explanation, which I thought seemed clever. Why is that wrong?

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Re: PS: Geometry   [#permalink] 30 Nov 2008, 10:20
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