Author 
Message 
TAGS:

Hide Tags

Retired Moderator
Status: The last round
Joined: 18 Jun 2009
Posts: 1279
Concentration: Strategy, General Management

If a right triangle has area 28 and hypotenuse 12, what is [#permalink]
Show Tags
13 Jun 2010, 04:04
10
This post was BOOKMARKED
Question Stats:
75% (02:03) correct 25% (02:24) wrong based on 248 sessions
HideShow timer Statistics
If a right triangle has area 28 and hypotenuse 12, what is its perimeter? A. 20 B. 24 C. 28 D. 32 E. 36
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
[ From 470 to 680My Story ] [ My Last Month Before Test ] [ GMAT Prep Analysis Tool ] [ US. Business School Dashboard ] [ Int. Business School Dashboard ]
I Can, I Will
GMAT Club Premium Membership  big benefits and savings
Last edited by Bunuel on 26 Dec 2013, 02:47, edited 1 time in total.
Renamed the topic, edited the question and added the OA.



Senior Manager
Joined: 30 Aug 2009
Posts: 280
Location: India
Concentration: General Management

Re: Doubtful PS [#permalink]
Show Tags
13 Jun 2010, 05:17
1
This post received KUDOS
2
This post was BOOKMARKED
Hussain15 wrote: If a right triangle has area 28 and hypotenuse 12, what is its perimeter?
A. 20 B. 24 C. 28 D. 32 E. 36 C  28 let the other 2 sides be a and b then we have 1/2 * a*b = 28 or a*b =56 also we have a^2 + b^2 = 144 adding 2ab to a^2 + b^2 we have a^2 + b^2 + 2ab = 144 + 2*56 = 256 => (a+b)^2 = 256 or a+ b = 16. So perimeter is a+b+ hypotenuse = 16+ 12 = 28



Math Expert
Joined: 02 Sep 2009
Posts: 43894

Re: Doubtful PS [#permalink]
Show Tags
13 Jun 2010, 05:27
3
This post received KUDOS
Expert's post
2
This post was BOOKMARKED



Retired Moderator
Status: The last round
Joined: 18 Jun 2009
Posts: 1279
Concentration: Strategy, General Management

Re: Doubtful PS [#permalink]
Show Tags
13 Jun 2010, 06:41
1
This post received KUDOS



Math Expert
Joined: 02 Sep 2009
Posts: 43894

Re: Doubtful PS [#permalink]
Show Tags
13 Jun 2010, 06:54



Retired Moderator
Status: The last round
Joined: 18 Jun 2009
Posts: 1279
Concentration: Strategy, General Management

Re: Doubtful PS [#permalink]
Show Tags
13 Jun 2010, 08:12
Thanks Bunuel!! Actually I started to solve this problem by using 3 4 5 formula of right triangle I.e 3^2+4^2= 5^2.This ended no where!! Posted from my mobile device
_________________
[ From 470 to 680My Story ] [ My Last Month Before Test ] [ GMAT Prep Analysis Tool ] [ US. Business School Dashboard ] [ Int. Business School Dashboard ]
I Can, I Will
GMAT Club Premium Membership  big benefits and savings



Intern
Joined: 25 Mar 2010
Posts: 1

Re: Doubtful PS [#permalink]
Show Tags
21 May 2011, 17:58
Apologies
Can someone explain why we are adding 2ab?
I don't understand that part.
Cheers



Math Forum Moderator
Joined: 20 Dec 2010
Posts: 1945

Re: Doubtful PS [#permalink]
Show Tags
21 May 2011, 22:33
1
This post was BOOKMARKED
k4lnamja wrote: Apologies
Can someone explain why we are adding 2ab?
I don't understand that part.
Cheers No need to be apologetic k4lnamja. You can ask any question so far it's related to the topic. We are dealing with a right angle triangle; We are given its area and the hypotenuse and we are asked for perimeter. Right angle triangle has three sides; one of which is hypotenuse. If we know the length of the other two, we will have the perimeter. However, there is no way to find out the length of the other two sides individually. Thus, our intention is to find the combined length of the other two sides and add it up with the hypotenuse to get the perimeter. How can we use the information to know the combined length of the other two sides. Here's how. Hypotenuse = c = 12 Let the other two sides of the right angle triangle be "a" and "b" and we know these two sides are perpendicular to each other. Area = 28 Area of a triangle = 1/2*base*height = 1/2*a*b 1/2*a*b=28 a*b=56 c=12 As per pythagoras: a^2+b^2=c^2 (a+b)^22ab=c^2 (a+b)^22*56=12^2 (a+b)^2112=144 (a+b)^2=256 a+b=16 Thus, we know the sum of other two sides. a+b=16 c=12 a+b+c=16+12=28 ****************** Ans: "C" ********************** Just to expand the formula used: (a+b)^2=a^2+b^2+2ab (a+b)^22ab=a^2+b^2 (a+b)^22ab=c^2 **********************
_________________
~fluke
GMAT Club Premium Membership  big benefits and savings



VP
Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 1260

Re: Doubtful PS [#permalink]
Show Tags
23 May 2011, 22:14
1
This post received KUDOS
1/2 * 12 * altitude = 28 altitude = 7 using similar triangle 7/x = x/12 gives x^2 = 84 12^2  84 = 60 thus 60 ^ (1/2) + 84 ^(1/2) + 12 = 28.7 approx. Hence C.
_________________
Visit  http://www.sustainablesphere.com/ Promote Green Business,Sustainable Living and Green Earth !!



Director
Joined: 01 Feb 2011
Posts: 703

Re: Doubtful PS [#permalink]
Show Tags
27 Aug 2011, 08:29
area = (1/2)bh = 28 => bh=56
hypotenuse = sqrt(b^2+h^2) = 12 => b^2+h^2 = 144
perimeter = b+h+sqrt(b^2+h^2)
we know that (b+h)^2 = b^2+h^2+2bh
= 144+2(56)
=> b+h = 16
=> perimeter = 16+12 = 28



Current Student
Joined: 04 May 2015
Posts: 73
Concentration: Strategy, Operations
WE: Operations (Military & Defense)

Re: If a right triangle has area 28 and hypotenuse 12, what is [#permalink]
Show Tags
16 Aug 2015, 17:08
amit2k9 wrote: 1/2 * 12 * altitude = 28 altitude = 7
using similar triangle
7/x = x/12 gives x^2 = 84
12^2  84 = 60
thus 60 ^ (1/2) + 84 ^(1/2) + 12 = 28.7 approx.
Hence C. I know it's been a long time since this post was made, but is anyone able to explain where 7/x = x/12 gives x^2 = 84 comes from??? I would like to try and understand this alternate approach that uses the hypotenuse as the base. Thanks!
_________________
If you found my post useful, please consider throwing me a Kudos... Every bit helps



Math Expert
Joined: 02 Sep 2009
Posts: 43894

Re: If a right triangle has area 28 and hypotenuse 12, what is [#permalink]
Show Tags
16 Aug 2015, 17:12



Current Student
Joined: 04 May 2015
Posts: 73
Concentration: Strategy, Operations
WE: Operations (Military & Defense)

Re: If a right triangle has area 28 and hypotenuse 12, what is [#permalink]
Show Tags
16 Aug 2015, 17:20
Bunuel wrote: DropBear wrote: amit2k9 wrote: 1/2 * 12 * altitude = 28 altitude = 7
using similar triangle
7/x = x/12 gives x^2 = 84
12^2  84 = 60
thus 60 ^ (1/2) + 84 ^(1/2) + 12 = 28.7 approx.
Hence C. I know it's been a long time since this post was made, but is anyone able to explain where 7/x = x/12 gives x^2 = 84 comes from??? I would like to try and understand this alternate approach that uses the hypotenuse as the base. Thanks! Crossmultiply \(\frac{7}{x} = \frac{x}{12}\) to get \(7*12=x*x\) > \(84=x^2\). Hi Bunuel, Thanks for the very quick reply. I understand the calculation, just not sure about how we use similar triangles to arrive at that line in the first place? Don't understand why we are doing \(\frac{7}{x} = \frac{x}{12}\) in the first place... Sorry if this seems rudimentary...
_________________
If you found my post useful, please consider throwing me a Kudos... Every bit helps



Current Student
Joined: 20 Mar 2014
Posts: 2683
Concentration: Finance, Strategy
GPA: 3.7
WE: Engineering (Aerospace and Defense)

Re: If a right triangle has area 28 and hypotenuse 12, what is [#permalink]
Show Tags
16 Aug 2015, 17:24
DropBear wrote: amit2k9 wrote: 1/2 * 12 * altitude = 28 altitude = 7
using similar triangle
7/x = x/12 gives x^2 = 84
12^2  84 = 60
thus 60 ^ (1/2) + 84 ^(1/2) + 12 = 28.7 approx.
Hence C. I know it's been a long time since this post was made, but is anyone able to explain where 7/x = x/12 gives x^2 = 84 comes from??? I would like to try and understand this alternate approach that uses the hypotenuse as the base. Thanks! I believe Bunuel has answered your question. As a matter of fact, the text in red above is incorrect. The altitude should be 14/3 and NOT 7 as it has been calculated. The final answer as well is an integer, dont know how is the poster getting a decimal value. IMO, the method is a 'forced' one as I am having difficulty in coming to the same equation for 'x'. Not a good method.



Current Student
Joined: 04 May 2015
Posts: 73
Concentration: Strategy, Operations
WE: Operations (Military & Defense)

If a right triangle has area 28 and hypotenuse 12, what is [#permalink]
Show Tags
16 Aug 2015, 17:50
Engr2012 wrote: DropBear wrote: amit2k9 wrote: 1/2 * 12 * altitude = 28 altitude = 7
using similar triangle
7/x = x/12 gives x^2 = 84
12^2  84 = 60
thus 60 ^ (1/2) + 84 ^(1/2) + 12 = 28.7 approx.
Hence C. I know it's been a long time since this post was made, but is anyone able to explain where 7/x = x/12 gives x^2 = 84 comes from??? I would like to try and understand this alternate approach that uses the hypotenuse as the base. Thanks! I believe Bunuel has answered your question. As a matter of fact, the text in red above is incorrect. The altitude should be 14/3 and NOT 7 as it has been calculated. The final answer as well is an integer, dont know how is the poster getting a decimal value. IMO, the method is a 'forced' one as I am having difficulty in coming to the same equation for 'x'. Not a good method. I completely overlooked that part in red, in that case 1/2 * 12 * altitude = 28 altitude = 4 2/3. However I will take your advice and leave this one alone as I don't want to confuse myself. Edit: Edited 4 3/2 to 4 2/3
_________________
If you found my post useful, please consider throwing me a Kudos... Every bit helps
Last edited by DropBear on 16 Aug 2015, 18:48, edited 1 time in total.



Current Student
Joined: 20 Mar 2014
Posts: 2683
Concentration: Finance, Strategy
GPA: 3.7
WE: Engineering (Aerospace and Defense)

Re: If a right triangle has area 28 and hypotenuse 12, what is [#permalink]
Show Tags
16 Aug 2015, 18:46
DropBear wrote:
I completely overlooked that part in red, in that case 1/2 * 12 * altitude = 28 altitude = 4 3/2. However I will take your advice and leave this one alone as I don't want to confuse myself. I believe you meant 4 2/3 instead of 4 3/2



Manager
Status: 2 months to go
Joined: 11 Oct 2015
Posts: 134
GPA: 3.8

If a right triangle has area 28 and hypotenuse 12, what is [#permalink]
Show Tags
26 Jul 2016, 13:16
1
This post received KUDOS
Another approach: GMAT loves special triangles and guess what this is a special triangle. With an hypotenuse of 12, the first thing that comes to my mind is a 30:60:90 triangle (l:l√3:2l), If this was the case, we would have: 2l= 12 l=6 l√3= 6√3 To test it we simply apply the pythagorean theorem, \(6^{2}+\left( 6\sqrt{3} \right)^{2}\; has\; to\; equal\; 12^{2}\; >\; \sqrt{36\; +\; 108}\; =\; \sqrt{144}\; >\; 12\; =\; 12\;\) \(>\; The\; right\; triangle\; is\; a\; 30:60:90\; triangle.\) Now that we know the measures of the sides we simply add them. 2p= 12+6*1,7 +6= 12 + 5*2 + 6 = 28. Answer C.



Intern
Joined: 06 Apr 2013
Posts: 2

Re: If a right triangle has area 28 and hypotenuse 12, what is [#permalink]
Show Tags
02 Oct 2016, 02:16
1
This post received KUDOS
what is wrong with this approach?
(1/2)*b*h=28 b*h = 56 now 56 can be broken down into following pairs 1, 56 2, 28 4, 14 8, 7 Since two sides of a triangle must be bigger than third side we can use 8,7 so the perimeter is 8+7+12=27 BUT 8^2 + 7^2 does not equal 144.
Where did I get it wrong??



Math Expert
Joined: 02 Sep 2009
Posts: 43894

Re: If a right triangle has area 28 and hypotenuse 12, what is [#permalink]
Show Tags
02 Oct 2016, 04:23



NonHuman User
Joined: 09 Sep 2013
Posts: 13775

Re: If a right triangle has area 28 and hypotenuse 12, what is [#permalink]
Show Tags
21 Jan 2018, 08:49
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: If a right triangle has area 28 and hypotenuse 12, what is
[#permalink]
21 Jan 2018, 08:49






