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

It is currently 20 Jul 2018, 11:41

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

In right angle triangle ABC, AB = 6, BC = 8 and AC = 10. A square PQRS

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

Hide Tags

Manager
Manager
User avatar
P
Joined: 22 Feb 2018
Posts: 187
In right angle triangle ABC, AB = 6, BC = 8 and AC = 10. A square PQRS  [#permalink]

Show Tags

New post 06 Jul 2018, 06:25
1
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

44% (01:32) correct 56% (03:09) wrong based on 9 sessions

HideShow timer Statistics

In right angle triangle ABC, AB = 6, BC = 8 and AC = 10. A square PQRS is inscribed in the triangle as shown in the figure. Find the side of the square?
Attachment:
Capture.PNG
Capture.PNG [ 4.97 KiB | Viewed 351 times ]


A) \(3\)
B) \(\frac{120}{37}\)
C) \(4\)
D) \(\frac{40}{9}\)
E) \(\frac{120}{23}\)

_________________

Good, good Let the kudos flow through you

DS Forum Moderator
User avatar
P
Joined: 27 Oct 2017
Posts: 623
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)
Premium Member CAT Tests
Re: In right angle triangle ABC, AB = 6, BC = 8 and AC = 10. A square PQRS  [#permalink]

Show Tags

New post 06 Jul 2018, 07:02
This question can be solved by using similarity of triangles, see the sketch attached.
Attachments

WhatsApp Image 2018-07-06 at 19.30.14.jpeg
WhatsApp Image 2018-07-06 at 19.30.14.jpeg [ 67.04 KiB | Viewed 322 times ]


_________________

SC: Confusable words
All you need for Quant, GMAT PS Question Directory,GMAT DS Question Directory
Error log/Key Concepts
Combination Concept: Division into groups
Question of the Day (QOTD)
Free GMAT CATS

Expert Post
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 6258
In right angle triangle ABC, AB = 6, BC = 8 and AC = 10. A square PQRS  [#permalink]

Show Tags

New post 07 Jul 2018, 01:48
Princ wrote:
In right angle triangle ABC, AB = 6, BC = 8 and AC = 10. A square PQRS is inscribed in the triangle as shown in the figure. Find the side of the square?
Attachment:
The attachment Capture.PNG is no longer available


A) \(3\)
B) \(\frac{120}{37}\)
C) \(4\)
D) \(\frac{40}{9}\)
E) \(\frac{120}{23}\)


If we look at sides as of \(\triangle{ABC}\), 6, 8, 10, it tells us that it is 3:4:5 triangle..

Now let side of square be x and PQ is || to AC (opposite sides of square)
in \(\triangle{BPQ}\), the sides too will be in 3:4:5 = BQ : BP : x
so BP = \(\frac{4x}{5}\)

now \(\triangle{CPS}\) and \(\triangle{ABC}\) are also similar and hence 3:4:5 \(\triangle\)
now 3:4:5=PS:CS:CP=x:CS:CP
so 3 = x, so 5 = CP = \(\frac{5x}{3}\)

Now BP+CP=AB...........\(\frac{4x}{5}+\frac{5x}{3}=8.................\frac{12x+25x}{15}=8..............\frac{37x}{15}=8\).
\(x=\frac{8*15}{37}=\frac{120}{37}\)

B
Attachments

Capture.PNG
Capture.PNG [ 13.79 KiB | Viewed 179 times ]


_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

Manager
Manager
User avatar
P
Joined: 22 Feb 2018
Posts: 187
Re: In right angle triangle ABC, AB = 6, BC = 8 and AC = 10. A square PQRS  [#permalink]

Show Tags

New post 07 Jul 2018, 02:45
OA: B
Given AB=6 ,BC = 8 , AC =10
Attachment:
Capture Ans.PNG
Capture Ans.PNG [ 14.06 KiB | Viewed 165 times ]

As can be seen from figure above, all four \(\triangle\) i.e. \(\triangle\)ABC ,\(\triangle\)ARQ ,\(\triangle\)QBP ,\(\triangle\) PSC are similar.
Because of AA similarity as their corresponding angles are equal in measure.

Considering \(\triangle\) ABC and \(\triangle\) QBP ,we get
\(\frac{BP}{BC}=\frac{BQ}{AB}=\frac{PQ}{AC} = k\) (a constant)

We get \(QP=10k\) and \(BQ=6k\)

As all sides of a square are equal,QR will be also equal to QP i.e \(QR =10k\).

Considering \(\triangle\) ABC and \(\triangle\) QBP ,we get
\(\frac{QR}{BC}=\frac{AR}{AB}=\frac{AQ}{AC} = p\) (a constant)
\(\frac{QR}{BC}=\frac{AQ}{AC}\)
\(\frac{{10k}}{8}=\frac{AQ}{10}\)
\(AQ =\frac{{100k}}{8}=\frac{{25k}}{2}\)

\(AB =BQ+AQ\)
\(6= 6k + \frac{{25k}}{2}\)
\(k = \frac{12}{37}\)

Side of Square\(= 10k = 10* \frac{12}{37} =\frac{120}{37}\)
_________________

Good, good Let the kudos flow through you

Re: In right angle triangle ABC, AB = 6, BC = 8 and AC = 10. A square PQRS &nbs [#permalink] 07 Jul 2018, 02:45
Display posts from previous: Sort by

In right angle triangle ABC, AB = 6, BC = 8 and AC = 10. A square PQRS

  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®.