Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 60460

If a triangle has sides 8, 10, and z, which of the following cannot be
[#permalink]
Show Tags
17 Sep 2018, 21:54
Question Stats:
52% (01:32) correct 48% (01:37) wrong based on 79 sessions
HideShow timer Statistics
If a triangle has sides 8, 10, and z, which of the following cannot be the area of the triangle? A. 3 B. 6 C. 12 D. 24 E. 46
Official Answer and Stats are available only to registered users. Register/ Login.
_________________



CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2981
Location: India
GMAT: INSIGHT
WE: Education (Education)

If a triangle has sides 8, 10, and z, which of the following cannot be
[#permalink]
Show Tags
18 Sep 2018, 01:10
Bunuel wrote: If a triangle has sides 8, 10, and z, which of the following cannot be the area of the triangle?
A. 3 B. 6 C. 12 D. 24 E. 46 Property : For given two sides of triangle and third side missing, the area of the triangle is maximum when the given two sides are perpendicular to each other. (Derivation attached)i.e. \(A_{max.} = (1/2)*8*10 = 40\) i.e. any number greater than 40 can NOT be area of this triangle Answer: Option E
Attachments
File comment: www.GMATinsight.com
Geometry Question.jpg [ 88.48 KiB  Viewed 863 times ]
_________________
Prosper!!!GMATinsightBhoopendra Singh and Dr.Sushma Jha email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne Skype based classes and Classroom Coaching in South and West Delhihttp://www.GMATinsight.com/testimonials.htmlACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 9031
Location: United States (CA)

Re: If a triangle has sides 8, 10, and z, which of the following cannot be
[#permalink]
Show Tags
23 Sep 2018, 16:38
Bunuel wrote: If a triangle has sides 8, 10, and z, which of the following cannot be the area of the triangle?
A. 3 B. 6 C. 12 D. 24 E. 46 If the triangle is a right triangle with z being the hypotenuse, then the two legs 10 and 8 will be the base and height of the triangle. In that case, the area of the triangle is ½ x 10 x 8 = 40. This is the maximum area for a triangle with two sides of 8 and 10; thus, any area less than 40 is a possible value for the area. Thus, answer choice E cannot be the area of the triangle. Answer: E
_________________
5star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews If you find one of my posts helpful, please take a moment to click on the "Kudos" button.



Intern
Joined: 15 Sep 2018
Posts: 31

Re: If a triangle has sides 8, 10, and z, which of the following cannot be
[#permalink]
Show Tags
27 Sep 2018, 01:00
When we know two of the side lengths, the greatest possible area of the triangle will occur when the two sides form a right triangle.
With \(8\) and \(10\) as the base and height of the triangle, we have an area of: Area = 1⁄2 × Base × Height \(Area = 1⁄2 × 8 × 10\) \(Area = 40\) Since the greatest possible area of the triangle with sides \(8\), \(10\), and \(z\) is \(40\), other smaller areas ARE possible (if we change the angle to something other than 90 degrees). Thus, it cannot have an area greater than \(40\). The final answer is .



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9983
Location: Pune, India

Re: If a triangle has sides 8, 10, and z, which of the following cannot be
[#permalink]
Show Tags
27 Sep 2018, 01:25
Bunuel wrote: If a triangle has sides 8, 10, and z, which of the following cannot be the area of the triangle?
A. 3 B. 6 C. 12 D. 24 E. 46 Just use logic. Think about it: given two sides and an unknown third  we can have a triangle with very very small area (almost 0), then the area increases and then finally starts decreasing again until it comes to 0 again. So there is a maximum limit to the area that the triangle can have. Hence given a range of increasing areas, the one which will not be possible is the largest one. For example, if 24 were not possible, 46 would not be possible too. But there is only one correct answer. Hence it must be 46 only. Attachment:
TrianglesForm.jpeg [ 40.37 KiB  Viewed 698 times ]
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



NonHuman User
Joined: 09 Sep 2013
Posts: 13959

Re: If a triangle has sides 8, 10, and z, which of the following cannot be
[#permalink]
Show Tags
23 Nov 2019, 12:26
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.
_________________




Re: If a triangle has sides 8, 10, and z, which of the following cannot be
[#permalink]
23 Nov 2019, 12:26






