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# Is the perimeter of triangle ABC greater than 20? 1. BC-AC =

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Is the perimeter of triangle ABC greater than 20? 1. BC-AC = [#permalink]

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30 Mar 2007, 15:01
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Is the perimeter of triangle ABC greater than 20?

1. BC-AC = 10
2. The area of the triangle is 20.

Can anyone plz help.
Thanks
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30 Mar 2007, 15:21
A

Suppose a,b,c are the lengths of 3 sides.
According to the length rules, c<a>a-b

1.BC-AC = 10. so 3rd side should be >10.
Minimum lengths of other 2 sides are 11,1 so perimeter is going to be greater than 20.

2.Are does say anything abt the perimeter.
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30 Mar 2007, 18:16
D???

Not using heron's theorem, to get an area of 20 in a triangle, base*height must equal 40.

Possible combinations are:
10*4
8*5

in either case, perimeter > 20
(used right and isoceles triangles)

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31 Mar 2007, 11:07
The answer is C, i am still not able to figure out how and why.

BV
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31 Mar 2007, 11:51
The OA is wrong...Should be A
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31 Mar 2007, 18:05
Yes, it should be 'A'.

BC-AC = 10
BC = AC + 10
BC > 10
To keep the perimeter minimum BC should be the largest side and AC be the smallest side. From the rule of triangle, the sum of the smaller side should be greater than the largest side. That means AB + AC > BC. So AB+ AC > 10.
AB+AC+BC > 20.
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01 Apr 2007, 06:22
Is the perimeter of triangle ABC greater than 20?

1. BC-AC = 10
2. The area of the triangle is 20.

from 1, BC-AC =10 and as 3 rd side is always larger than diff of two sides. BC-AC<AB>10 and BC =10+AC so BC>10 so perimeter > 20 =>it is sufficient

from 2,
perimeter will be minimum if triangle is equilateral and equilateral triangle give permiter>20 so it is also sufficient

so I would go with D

01 Apr 2007, 06:22
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