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

It is currently 21 Sep 2018, 16:36

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

A right triangle has sides 6, a and 10. If the area of the triangle i

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

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49300
A right triangle has sides 6, a and 10. If the area of the triangle i  [#permalink]

Show Tags

New post 23 Aug 2018, 03:51
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

68% (00:42) correct 32% (00:37) wrong based on 22 sessions

HideShow timer Statistics

Director
Director
User avatar
P
Status: Learning stage
Joined: 01 Oct 2017
Posts: 856
WE: Supply Chain Management (Energy and Utilities)
Premium Member CAT Tests
Re: A right triangle has sides 6, a and 10. If the area of the triangle i  [#permalink]

Show Tags

New post 23 Aug 2018, 04:06
Bunuel wrote:
A right triangle has sides 6, a and 10. If the area of the triangle is less than 30, what is the value of a?

A. 3
B. 4
C. 5
D. 8
E. 11.6


range of a
\((10-6) < a <(10+6)\)
Or, 4 < a < 16

Given Area < 30

6,8,10 is a Pythagoras triplet with area=1/2*6*8=24<30

So the value of a is 8.

Ans. (D)
_________________

Regards,

PKN

Rise above the storm, you will find the sunshine

Board of Directors
User avatar
P
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4032
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
GMAT ToolKit User Premium Member
Re: A right triangle has sides 6, a and 10. If the area of the triangle i  [#permalink]

Show Tags

New post 23 Aug 2018, 07:34
Bunuel wrote:
A right triangle has sides 6, a and 10. If the area of the triangle is less than 30, what is the value of a?

A. 3
B. 4
C. 5
D. 8
E. 11.6


\(\frac{1}{2}*6*10 = 30\) ( So, 10 is not the Base or altitude of the triangle )

Further the value of the third side must be \(10 - 6 < a < 10 + 6\) or, \(4 < a < 16\) ( Options A and B can be eliminated )

If one is through with the concept of Pythagorean triplets he can easily recall the other side, without even calculating ( 6, 8 , 10 )

So, The value of \(a = 8\), Answer must be (D)
_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

Senior SC Moderator
avatar
V
Joined: 22 May 2016
Posts: 1978
Premium Member CAT Tests
A right triangle has sides 6, a and 10. If the area of the triangle i  [#permalink]

Show Tags

New post 26 Aug 2018, 17:55
Bunuel wrote:
A right triangle has sides 6, a and 10. If the area of the triangle is less than 30, what is the value of a?

A. 3
B. 4
C. 5
D. 8
E. 11.6

I. Right triangle ratio rule

Another way: use a property of 3-4-5 right triangles, listed below.

Because the area of the right triangle is less than 30, the side with length 10 is the hypotenuse.

If the given sides were legs (which, in a right triangle, are base and height), area would be \(\frac{(6 * 10)}{2}=30\). Not allowed.

\(a\) cannot be greater than 10. If \(a\) were greater than 10, \(a\) would be the hypotenuse, and area would \(=30\)

The side with length of 10 must be the hypotenuse. The side with length of 6 is a leg.

Rule: in a right triangle, if one leg and the hypotenuse are in the ratio \(3x:5x\) or \(4x:5x\), the triangle is a \(3x-4x-5x\) right triangle.

In this instance, the ratio of leg to hypotenuse is \(3x:5x\)
\(3x=6\), so \(x=2\) (or \(5x=10\), so \(x=2\))
\(a\) = the missing ratio part from the rule: \(4x\)
Leg \(a=(4*2)=8\)

Answer D

Pythagorean theorem
Alternatively, use area limit and the Pythagorean theorem to find \(a\)

Area, A = \(\frac{b*h}{2}<30\). If the given sides were legs, area would = \(\frac{6*10}{2}=30\)

\(a\) cannot be greater than 10. If \(a\) were greater than 10, \(a\) would be the hypotenuse, and area would \(=30\)

The side with length of 6 is a leg
The side with length of 10 is the hypotenuse

Pythagorean theorem: \((6^2+ a^2)=10^2\)
\(a^2=(100-36)\)
\(a^2=64\)
\(a=8\)

Answer D
_________________

In the depths of winter, I finally learned
that within me there lay an invincible summer.

-- Albert Camus, "Return to Tipasa"

Target Test Prep Representative
User avatar
G
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 3515
Location: United States (CA)
Re: A right triangle has sides 6, a and 10. If the area of the triangle i  [#permalink]

Show Tags

New post 26 Aug 2018, 19:19
Bunuel wrote:
A right triangle has sides 6, a and 10. If the area of the triangle is less than 30, what is the value of a?

A. 3
B. 4
C. 5
D. 8
E. 11.6


Recall that the sum of the lengths of the two shorter sides of a triangle must be greater than the length of the longest side; thus, a could be 5 (since 6 + 5 > 10) or 8 (since 6 + 8 > 10) or 11.6 (since 6 + 10 > 11.6). We can eliminate choices A and B.

However, a could not be 5 since the triangle is a right triangle and 6^2 + 5^2 ≠ 10^2. We can eliminate answer choice C. On the other hand, a could be 8 since 6^2 + 8^2 = 10^2 or a could be 11.6 since 6^2 + 100^2 = 11.6^2 (if we ignore round-off error).

Lastly, the area of a right triangle is ½ the product of the lengths of its two legs. If a = 8, then the area of the triangle is ½(6)(8) = 24. Similarly, if a = 10, then the area of the triangle is ½(6)(10) = 30. However, since we are given that the area of the triangle is less than 30, a must be 8.

Answer: D
_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Re: A right triangle has sides 6, a and 10. If the area of the triangle i &nbs [#permalink] 26 Aug 2018, 19:19
Display posts from previous: Sort by

A right triangle has sides 6, a and 10. If the area of the triangle i

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

Events & Promotions

PREV
NEXT


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.