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In triangle ABC, AB = 30. AC = 28. If the area of the triangle is 336,

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In triangle ABC, AB = 30. AC = 28. If the area of the triangle is 336,  [#permalink]

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New post Updated on: 02 Oct 2018, 06:20
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A
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D
E

Difficulty:

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Question Stats:

54% (02:45) correct 46% (02:33) wrong based on 54 sessions

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In triangle ABC, AB = 30. AC = 28. If the area of the triangle is 336, what is the perimeter of the triangle?

A. 58
B. 77
C. 82
D. 84
E. 92

Originally posted by arnavrayaca on 02 Oct 2018, 03:51.
Last edited by Bunuel on 02 Oct 2018, 06:20, edited 1 time in total.
Renamed the topic and edited the question.
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Re: In triangle ABC, AB = 30. AC = 28. If the area of the triangle is 336,  [#permalink]

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New post 02 Oct 2018, 07:35
arnavrayaca wrote:
In triangle ABC, AB = 30. AC = 28. If the area of the triangle is 336, what is the perimeter of the triangle?

A. 58
B. 77
C. 82
D. 84
E. 92


Formula used:- Area of scalene triangle=\(\sqrt{s(s-a)(s-b)(s-c)}\)
Here, a=28, b=30, c=x(say)
\(s=\frac{a+b+c}{2}=29+\frac{x}{2}\)

So, \((29+\frac{x}{2})(29-\frac{x}{2})(\frac{x}{2}+1)(\frac{x}{2}-1)=336^2\)
Or, \(\left(29^2-\frac{x^2}{4}\right)\left(\frac{x^2}{4}-1\right)=336^2\)
Solving for x, we have x=26.

Hence perimeter=26+28+30=84

Ans. (D)
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In triangle ABC, AB = 30. AC = 28. If the area of the triangle is 336,  [#permalink]

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New post 22 Mar 2019, 04:34
1
Bunuel Can you help with this question. I am not able to understand how to go about this question without using the formula.

I can find the third side must be between 2<third side<58 and this means that the perimeter can range from 58+3 =61 to 58+57 = 115. We don't know which side is the base or any angles. Please help!

How can we solve this question without using the area of scalene triangle formula? Bunuel
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Re: In triangle ABC, AB = 30. AC = 28. If the area of the triangle is 336,  [#permalink]

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New post 22 Mar 2019, 05:14
we have to use hero's formula

when three sides are given , we can find the area using this formula

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Re: In triangle ABC, AB = 30. AC = 28. If the area of the triangle is 336,  [#permalink]

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New post 13 May 2019, 01:54
harasali91 wrote:
Bunuel Can you help with this question. I am not able to understand how to go about this question without using the formula.

I can find the third side must be between 2<third side<58 and this means that the perimeter can range from 58+3 =61 to 58+57 = 115. We don't know which side is the base or any angles. Please help!

How can we solve this question without using the area of scalene triangle formula? Bunuel


The question can be solved via other methods but it would take a lot of effort and time which you wont get on GMAT.
Since the area of the triangle is known, we can find the altitudes by considering the known sides, each at time, subsequently you can form equations and solve for variables.
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Re: In triangle ABC, AB = 30. AC = 28. If the area of the triangle is 336,  [#permalink]

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New post 13 May 2019, 02:54
Area= 0.5*30*28 sinx=336
sinx=4/5
cosx=3/5

cosx= (30^2 + 28^2 - BC^2)/2*30*28 (cosine formula)
3/5= (900+784- BC^2)/60*28
BC^2=676
BC=26

Perimeter= 26+28+30=84
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Re: In triangle ABC, AB = 30. AC = 28. If the area of the triangle is 336,  [#permalink]

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New post 16 May 2019, 22:06
Bunuel is there any other way to solve this question rather than using hero's formula.
This method of formula makes it very calculation intensive. Any other way to solve it?
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Re: In triangle ABC, AB = 30. AC = 28. If the area of the triangle is 336,  [#permalink]

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New post 16 May 2019, 22:16
Brother find the sine angle with the formula
Area of triangle=1/2 * b*c*sinA

You know sinA now, find cosA

And then use cosine formula to find third side

CosA= (b^2 + c^2 -a^2)/2bc
You will get a

globaldesi wrote:
Bunuel is there any other way to solve this question rather than using hero's formula.
This method of formula makes it very calculation intensive. Any other way to solve it?
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Re: In triangle ABC, AB = 30. AC = 28. If the area of the triangle is 336,  [#permalink]

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New post 18 May 2019, 06:20
nick1816 wrote:
Brother find the sine angle with the formula
Area of triangle=1/2 * b*c*sinA

You know sinA now, find cosA

And then use cosine formula to find third side

CosA= (b^2 + c^2 -a^2)/2bc
You will get a

globaldesi wrote:
Bunuel is there any other way to solve this question rather than using hero's formula.
This method of formula makes it very calculation intensive. Any other way to solve it?

Thanks [quote="nick1816"]
But since GMAT doesnt give the problems for sin cos. that means either there should be a way to solve this without the trigno functions or its too lengthy to solve without using the functions
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Re: In triangle ABC, AB = 30. AC = 28. If the area of the triangle is 336,  [#permalink]

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New post 20 May 2019, 13:14
What is the source of this problem? I've never seen a GMAT problem require the scalene formula until now this doesn't seem like a reasonable question to review.
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Re: In triangle ABC, AB = 30. AC = 28. If the area of the triangle is 336,  [#permalink]

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New post 21 May 2019, 00:45
Bunuel I'm Not able to understand by previous explanation given, Is there any other way to solve this question.
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Re: In triangle ABC, AB = 30. AC = 28. If the area of the triangle is 336,   [#permalink] 21 May 2019, 00:45
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