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by Bek » Wed Sep 07, 2011 5:54 pm
Can we calculate the area of a triangle knowing only its perimeter?
Last edited by Bek on Mon Oct 24, 2011 10:37 am, edited 1 time in total.
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by pemdas » Wed Sep 07, 2011 8:23 pm
a triangle's square is (1/2) * height*base, in isosceles triangle height=bisector

since triangle abc is isosceles, a=b, c is base and h is height we infer sqroot[a^2-(c^2/4)]=h and abc square will be c*sqroot[a^2-(c^2/4)]=36

we need to find perimeter (abc) or p=2a+c

from square (abc), sqroot[4a^2-c^2]=72/c ==> sqroot[(2a+c)(2a-c)]=72/c ==> sqroot(2a+c)=72/[c*sqroot(2a-c)] ==> 2a+c=(72^2)/[c^2*(2a-c)]





Bek wrote:If the area of an isosceles triangle is 18, what is its perimeter?

I couldn't handle it. Also I don't have the answer and answer choices.
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by saketk » Thu Sep 08, 2011 12:14 am
Bek wrote:If the area of an isosceles triangle is 18, what is its perimeter?

I couldn't handle it. Also I don't have the answer and answer choices.
there could be many answers to this question. If I cosider this triange a Right angled triangle then finding the sides is easier than when I consider some other shapes.

Area is 18 = 1/2*6*6 => the 3rd side will be -- 6sqrt(2)

Perimeter = 12+ 6sqrt(2)

or, use the Hero's forumula, where S= semi-perimeter of the triangle i.e. s= (2a+b)/2
&,
Area = sqrt[s(s-a)(s-a)(s-b)]
18 = (s-a)sqrt[s(s-b)]
This will give a value of a in terms of b. i.e. a relation, but no absolute answer.

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by GMATGuruNY » Thu Sep 08, 2011 3:22 am
Bek wrote:If the area of an isosceles triangle is 18, what is its perimeter?

I couldn't handle it. Also I don't have the answer and answer choices.
To answer the question, more information is needed.
An infinite number of isosceles triangles have an area of 18, so different perimeters are possible.
Two examples:

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by navami » Thu Sep 08, 2011 6:15 am
Is it isosceles or equilateral triangle?
This time no looking back!!!
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by Bek » Thu Sep 08, 2011 7:15 am
Thank you for your prompt reply. I will check the question, but I believe there wasn't any additional information.


GMATGuruNY wrote:
Bek wrote:If the area of an isosceles triangle is 18, what is its perimeter?



I couldn't handle it. Also I don't have the answer and answer choices.
To answer the question, more information is needed.
An infinite number of isosceles triangles have an area of 18, so different perimeters are possible.
Two examples:

Image
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by Bek » Thu Sep 08, 2011 7:16 am
It is isosceles


navami wrote:Is it isosceles or equilateral triangle?
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