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

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Intern
Joined: 14 Apr 2012
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What are the lengths of sides NO and OP in triangle NOP [#permalink]

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14 Apr 2012, 01:52
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60% (01:59) correct 40% (01:55) wrong based on 8 sessions

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

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

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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.
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14 Apr 2012, 02:27
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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)
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Triangle.png [ 8.01 KiB | Viewed 36509 times ]

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14 Apr 2012, 02:36
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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.
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Re: What are the lengths of sides NO and OP in triangle NOP [#permalink]

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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

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

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