GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 20 Aug 2019, 00:37

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

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

### Show Tags

Updated on: 02 Oct 2018, 06:20
13
00:00

Difficulty:

85% (hard)

Question Stats:

50% (02:53) correct 50% (02:33) wrong based on 50 sessions

### HideShow timer Statistics

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.
VP
Status: Learning stage
Joined: 01 Oct 2017
Posts: 1031
WE: Supply Chain Management (Energy and Utilities)
Re: In triangle ABC, AB = 30. AC = 28. If the area of the triangle is 336,  [#permalink]

### Show Tags

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)
_________________
Regards,

PKN

Rise above the storm, you will find the sunshine
Intern
Joined: 09 Mar 2018
Posts: 4
In triangle ABC, AB = 30. AC = 28. If the area of the triangle is 336,  [#permalink]

### Show Tags

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
Senior Manager
Joined: 25 Feb 2019
Posts: 337
Re: In triangle ABC, AB = 30. AC = 28. If the area of the triangle is 336,  [#permalink]

### Show Tags

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

Posted from my mobile device
Intern
Joined: 24 Dec 2018
Posts: 35
Re: In triangle ABC, AB = 30. AC = 28. If the area of the triangle is 336,  [#permalink]

### Show Tags

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.
_________________
+1 Kudos if you like the Question
Director
Joined: 19 Oct 2018
Posts: 770
Location: India
Re: In triangle ABC, AB = 30. AC = 28. If the area of the triangle is 336,  [#permalink]

### Show Tags

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
Director
Joined: 28 Jul 2016
Posts: 542
Location: India
Concentration: Finance, Human Resources
GPA: 3.97
WE: Project Management (Investment Banking)
Re: In triangle ABC, AB = 30. AC = 28. If the area of the triangle is 336,  [#permalink]

### Show Tags

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?
Director
Joined: 19 Oct 2018
Posts: 770
Location: India
Re: In triangle ABC, AB = 30. AC = 28. If the area of the triangle is 336,  [#permalink]

### Show Tags

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?
Director
Joined: 28 Jul 2016
Posts: 542
Location: India
Concentration: Finance, Human Resources
GPA: 3.97
WE: Project Management (Investment Banking)
Re: In triangle ABC, AB = 30. AC = 28. If the area of the triangle is 336,  [#permalink]

### Show Tags

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
Intern
Joined: 07 Mar 2019
Posts: 29
Re: In triangle ABC, AB = 30. AC = 28. If the area of the triangle is 336,  [#permalink]

### Show Tags

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.
Manager
Joined: 16 Aug 2014
Posts: 50
Re: In triangle ABC, AB = 30. AC = 28. If the area of the triangle is 336,  [#permalink]

### Show Tags

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.
_________________
Hit Kudos if you like the post
Re: In triangle ABC, AB = 30. AC = 28. If the area of the triangle is 336,   [#permalink] 21 May 2019, 00:45
Display posts from previous: Sort by

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne