WHat is the length of QS

Oldest

Best Reply

Author

Message

TAGS:

Director

Joined: 20 Jul 2004

Posts: 601

Followers: 1

Kudos [?]: 3 [0], given: 0

WHat is the length of QS [#permalink]

06 Oct 2004, 14:19

00:00

Question Stats:

0% (00:00) correct

0% (00:00) wrong

based on 0 sessions

WHat is the length of QS?

Attachments

DS8.JPG [ 3.68 KiB | Viewed 384 times ]

GMAT Club Legend

Joined: 15 Dec 2003

Posts: 4441

Followers: 10

Kudos [?]: 82 [0], given: 0

[#permalink]

06 Oct 2004, 15:12

12/5
1) 3^2 - (5-SR)^2 = QS^2
2) 4^2 - SR^2 = QS^2

Solve for SR and you get SR = 16/5
QS^2 = 4^2 - (16/5)^2
QS = 12/5

Quite calculation intensive. Took me about 3 min.
_________________

Best Regards,

Paul

Director

Joined: 08 Jul 2004

Posts: 613

Followers: 1

Kudos [?]: 4 [0], given: 0

[#permalink]

06 Oct 2004, 15:32

12/5 is 2.4. Is there any smarter way to do this which is being tested?
S

Director

Joined: 31 Aug 2004

Posts: 619

Followers: 1

Kudos [?]: 8 [0], given: 0

[#permalink]

06 Oct 2004, 15:37

It is an homothetic right angled triangle in another one :

so QS = 3*4/5 = 12/5

Director

Joined: 08 Jul 2004

Posts: 613

Followers: 1

Kudos [?]: 4 [0], given: 0

[#permalink]

06 Oct 2004, 15:43

Twixt, can you plz explain the concept mate?

Director

Joined: 31 Aug 2004

Posts: 619

Followers: 1

Kudos [?]: 8 [0], given: 0

[#permalink]

06 Oct 2004, 16:00

Saurya,

PQR and PQS have same lengths regardless the homothetic (al ?) ratio.

PS is similar to PQ rgdless ratio
QS QR ..........
PQ PR .............

so QS = QR * ratio

ratio = PQ/PR = 3 / 5

Manager

Joined: 27 Aug 2004

Posts: 158

Location: US

Followers: 1

Kudos [?]: 0 [0], given: 0

[#permalink]

06 Oct 2004, 18:58

I used area formula to get it

(1/2)*3*4 = (1/2)*5*x

you will get 12/5 =>2.4

GMAT Club Legend

Joined: 15 Dec 2003

Posts: 4441

Followers: 10

Kudos [?]: 82 [0], given: 0

[#permalink]

06 Oct 2004, 19:01

crackgmat3 wrote:

I used area formula to get it

(1/2)*3*4 = (1/2)*5*x

you will get 12/5 =>2.4

Nice crackgmat3! :cool

_________________

Best Regards,

Paul

Manager

Joined: 07 Sep 2004

Posts: 62

Followers: 1

Kudos [?]: 0 [0], given: 0

[#permalink]

06 Oct 2004, 23:51

There is a formula from grade 9 of how to find it.

1/QS^2 = 1/QP^2 + 1/QR^2 (I call it the umbrella formula)

applies for a right triangle with an altitude relative to hypotenuse

evrything can solve it .

Joined: 13 Jun 2004

Posts: 1134

Location: London, UK

Schools: Tuck'08

Followers: 5

Kudos [?]: 14 [0], given: 0

[#permalink]

10 Oct 2004, 23:15

I found a fastest and easier way and I am quite surprised because usually I am not so strong in Quant :roll:

Area of the triangle is (B*h)/2 and you can use different "h", there are 3 in every triangle. In this triangle there is QS but also QR and another one that is not drawn (from point P to somewhere in QR where it will be perpendicular) but we don't really care about the last one so it's ok :wink:

Area of PQR is (3*4)/2 = 6 (using QR as "h")

The area has to be the same so you can find QS by replacing the data : (5* QS)/2 = 12/5

Sounds ok to me, is there any objection ?

Ps : sorry, just realized crackgmat3 used the same way...I don't delete my post, the explanations are worth it :-D

Joined: 31 Dec 1969

Location: United States

Concentration: Marketing, Other

GMAT 1: 710 Q49 V38

WE: Accounting (Accounting)

Followers: 0

Kudos [?]: 32 [0], given: 54471

[#permalink]

11 Oct 2004, 14:04

it will be helpful to remember the following:

we can say 2 triangles are similar if two angles of one triangle are equal to two angles of another triangle.

Having said that,
triangle pqr and qsr(or qsp) are similar

reason:
ang pqr = 90 = ang qsr
ang prq = ang qrs (they represent the same angle in the figure)

now because of that since corresponding sides are proportional,
qs/4 = 3/5

so qs = 12/5

:-D

-anish

saurya_s wrote:

Twixt, can you plz explain the concept mate?

[#permalink] 11 Oct 2004, 14:04

		Similar topics	Author	Replies	Last post
Similar Topics:		What is length of hypotenuse	humans	3	24 Jun 2006, 21:23
	5	What is the length of segment BC?	GMAT TIGER	27	08 May 2008, 21:28
		In the figure shown, the length of line segment QS is	siddhans	3	23 Jul 2011, 20:47
		What is the length of the chord AB	kenguva	6	29 Jan 2012, 23:52
	5	In the diagram, what is the length of AB?	enigma123	14	05 Feb 2012, 17:30

WHat is the length of QS

Main navigation

GMAT Resources

Partners

MBA Resources

GMAT ® is a registered trademark of the Graduate Management Admission Council ® (GMAC ®). GMAT Club's website has not been reviewed or endorsed by GMAC.

GMAT Courses

Admissions Consulting

WHat is the length of QS

WHat is the length of QS

Main navigation

GMAT Resources

Partners

MBA Resources