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# PS: Geometry

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SVP
Joined: 21 Jul 2006
Posts: 1508

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29 Nov 2008, 05:09
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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
Manager
Joined: 27 May 2008
Posts: 200

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29 Nov 2008, 05:49

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
Manager
Joined: 18 Nov 2008
Posts: 115

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29 Nov 2008, 05:58
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.
Current Student
Joined: 28 Dec 2004
Posts: 3342
Location: New York City
Schools: Wharton'11 HBS'12

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29 Nov 2008, 07:41
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
SVP
Joined: 29 Aug 2007
Posts: 2467

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29 Nov 2008, 10:06
1
KUDOS
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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SVP
Joined: 21 Jul 2006
Posts: 1508

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29 Nov 2008, 11:39
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.
Retired Moderator
Joined: 18 Jul 2008
Posts: 959

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30 Nov 2008, 09:20
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?
Re: PS: Geometry   [#permalink] 30 Nov 2008, 09:20
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