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Difficulty:
35%
(medium)
Question Stats:
77% (02:13) correct
23%
(02:22)
wrong
based on 93
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What are the lengths of sides NO and OP in triangle NOP below?
A. \(NO = 10\) and \(OP=10\sqrt{34}\)
B. \(NO = 15\) and \(OP=10\sqrt{34}\)
C. \(NO = 20\) and \(OP=10\sqrt{34}\)
D. \(NO = 25\) and \(OP=10\sqrt{34}\)
E. \(NO = 30\) and \(OP=10\sqrt{34}\)
A. \(NO = 10\) and \(OP=10\sqrt{34}\)
B. \(NO = 15\) and \(OP=10\sqrt{34}\)
C. \(NO = 20\) and \(OP=10\sqrt{34}\)
D. \(NO = 25\) and \(OP=10\sqrt{34}\)
E. \(NO = 30\) and \(OP=10\sqrt{34}\)
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File comment: Image of problem.
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DSC00023.jpg [ 448.81 KiB | Viewed 70998 times ]
14 Apr 2012, 02:36
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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.
General Discussion
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)
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 69208 times ]
