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geometry - need help - please Experts!
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pemdas
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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)]
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
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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.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.
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
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To answer the question, more information is needed.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.
An infinite number of isosceles triangles have an area of 18, so different perimeters are possible.
Two examples:
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I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
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Bek
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Thank you for your prompt reply. I will check the question, but I believe there wasn't any additional information.
GMATGuruNY wrote:To answer the question, more information is needed.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.
An infinite number of isosceles triangles have an area of 18, so different perimeters are possible.
Two examples:
