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

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Intern
Joined: 29 Sep 2015
Posts: 3
In triangle ABC, AB = 30. AC = 28. If the area of the triangle is 336,  [#permalink]

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Updated on: 02 Oct 2018, 06:20
7
00:00

Difficulty:

75% (hard)

Question Stats:

42% (01:24) correct 58% (02:11) wrong based on 26 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.
Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 908
WE: Supply Chain Management (Energy and Utilities)
Re: In triangle ABC, AB = 30. AC = 28. If the area of the triangle is 336,  [#permalink]

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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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Re: In triangle ABC, AB = 30. AC = 28. If the area of the triangle is 336, &nbs [#permalink] 02 Oct 2018, 07:35
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