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geometry - need help - please Experts!

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Bek: Senior | Next Rank: 100 Posts; Posts: 68; Joined: Fri Dec 03, 2010 10:29 pmFollowed by: 1 member; Thanked: 5 times

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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pemdas: Legendary Member; Posts: 1084; Joined: Fri Apr 15, 2011 2:33 pmFollowed by: 21 members; Thanked: 158 times

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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saketk: Legendary Member; Posts: 608; Joined: Sun Jun 19, 2011 11:16 amFollowed by: 8 members; Thanked: 37 times

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.

What is the source of this question ?[/img]

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

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.
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navami: Legendary Member; Posts: 540; Joined: Sat Dec 20, 2008 7:24 pmFollowed by: 6 members; Thanked: 37 times

by navami » Thu Sep 08, 2011 6:15 am

Is it isosceles or equilateral triangle?

This time no looking back!!!
Navami

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Bek: Senior | Next Rank: 100 Posts; Posts: 68; Joined: Fri Dec 03, 2010 10:29 pmFollowed by: 1 member; Thanked: 5 times

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:

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Bek: Senior | Next Rank: 100 Posts; Posts: 68; Joined: Fri Dec 03, 2010 10:29 pmFollowed by: 1 member; Thanked: 5 times

by Bek » Thu Sep 08, 2011 7:16 am

It is isosceles

navami wrote:Is it isosceles or equilateral triangle?

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