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

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Intern
Joined: 18 Feb 2007
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Is the perimeter of triangle ABC greater than 20? 1. BC-AC = [#permalink]  30 Mar 2007, 15:01
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
Manager
Joined: 04 Jan 2006
Posts: 58
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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.
Senior Manager
Joined: 11 Feb 2007
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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)

Intern
Joined: 18 Feb 2007
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The answer is C, i am still not able to figure out how and why.

BV
VP
Joined: 28 Mar 2006
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The OA is wrong...Should be A
Director
Joined: 14 Jan 2007
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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.
Manager
Joined: 26 Feb 2007
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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

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