It is currently 20 Oct 2017, 04:00

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

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

What are the lengths of sides NO and OP in triangle NOP

Author Message
TAGS:

Hide Tags

Intern
Joined: 14 Apr 2012
Posts: 2

Kudos [?]: [0], given: 1

What are the lengths of sides NO and OP in triangle NOP [#permalink]

Show Tags

14 Apr 2012, 01:52
1
This post was
BOOKMARKED
00:00

Difficulty:

(N/A)

Question Stats:

60% (01:59) correct 40% (01:55) wrong based on 8 sessions

HideShow timer Statistics

What are the lengths of sides NO and OP in triangle NOP below?

[Reveal] Spoiler:
NO = 30 & OP = 10 (root)34

Attachments

File comment: Image of problem.

DSC00023.jpg [ 448.81 KiB | Viewed 36603 times ]

Last edited by Bunuel on 15 Nov 2013, 01:33, edited 2 times in total.
Edited the question

Kudos [?]: [0], given: 1

SVP
Joined: 16 Nov 2010
Posts: 1597

Kudos [?]: 592 [1], given: 36

Location: United States (IN)
Concentration: Strategy, Technology

Show Tags

14 Apr 2012, 02:27
1
KUDOS
Because the triangles are similar :
NO/PN = QR/PR
NO/24 = 50/40
NO = 30
Now OP = sqrt(50^2 + 30^2)
=> PQ = 10sqrt(34)
Attachments

Triangle.png [ 8.01 KiB | Viewed 36509 times ]

_________________

Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

GMAT Club Premium Membership - big benefits and savings

Kudos [?]: 592 [1], given: 36

Math Expert
Joined: 02 Sep 2009
Posts: 41892

Kudos [?]: 128947 [2], given: 12185

Show Tags

14 Apr 2012, 02:36
2
KUDOS
Expert's post
pashmi wrote:
Hi,

I need help solving the problem number 8 of the image attached in this post.

The answer is NO = 30 & OP = 10 (root)34

Thanks,
Pashmi

Welcome to GMAT Club. Below is a solution to your question.

What are the lengths of sides NO and OP in triangle NOP below?

Notice that triangles NOP and the smaller triangle within it (with the lengths of sides 24 and 40) are similar: they share the same angle P and both are right angled, so all their three angles are equal.

In similar triangles the ratio of the corresponding sides are equal (corresponding sides are the sides opposite the same angles). So, $$\frac{NO}{24}=\frac{NP}{40}$$ --> $$\frac{NO}{24}=\frac{40+10}{40}$$ --> $$NO=30$$.

Next, since $$NO=30$$ then $$OP=\sqrt{NO^2+NP^2}=\sqrt{30^2+50^2}=10\sqrt{34}$$.

Hope it's clear.

P.S. Please post PS questions in the PS subforum: gmat-problem-solving-ps-140/ and DS questions in the DS subforum: gmat-data-sufficiency-ds-141/ No posting of PS/DS questions is allowed in the main Math forum.
_________________

Kudos [?]: 128947 [2], given: 12185

Intern
Joined: 14 Apr 2012
Posts: 2

Kudos [?]: [0], given: 1

Re: What are the lengths of sides NO and OP in triangle NOP [#permalink]

Show Tags

14 Apr 2012, 07:36
Thanks Subhash!

Your solution makes me realize how easy it was. Thanks a ton!

Bunuel,

Thanks! I will keep the specification in mind from now on

Pashmi

Kudos [?]: [0], given: 1

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16640

Kudos [?]: 273 [0], given: 0

Re: What are the lengths of sides NO and OP in triangle NOP [#permalink]

Show Tags

14 Nov 2013, 18:15
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.
_________________

Kudos [?]: 273 [0], given: 0

Re: What are the lengths of sides NO and OP in triangle NOP   [#permalink] 14 Nov 2013, 18:15
Display posts from previous: Sort by