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

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Bunuel
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What are the lengths of sides NO and OP in triangle NOP below? [#permalink] New post   26 May 2019, 23:12
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What is the length of side OP in triangle NOP below?


A. 10
B. 30
C. \(\sqrt{34}\)
D. \(5\sqrt{34}\)
E. \(10\sqrt{34}\)

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#GREexcecise What are the lengths of sides NO and OP in triangle NOP below.jpg
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LeoN88
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What are the lengths of sides NO and OP in triangle NOP below? [#permalink] New post   26 May 2019, 23:23
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Bunuel wrote:
What is the length of side OP in triangle NOP below?


A. 10
B. 30
C. \(\sqrt{34}\)
D. \(5\sqrt{34}\)
E. \(10\sqrt{34}\)

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Attachment:
#GREexcecise What are the lengths of sides NO and OP in triangle NOP below.jpg


The small and big triangles are similar. Similar triangles have corresponding sides proportional-

40/50 = 24/NO
x= OP
So, NO = 30, now applying pythagoras

x^2 = 50^2 + 30^2
x^2 = 2500 + 900 =3400
x= 10 root(34) E
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What are the lengths of sides NO and OP in triangle NOP below? [#permalink] New post   27 May 2019, 02:39
Leo has given a perfect solution.

Just adding up.

Hypotenuse of smaller triangle with sides 24 and 32 will be 32.
(Note 24 and 32 are triplets of the form 3,4,5 ) where multiplication factor is 8 so no need to do calculation with SQRT formula.


Now, the hypotenuse of larger triangle that is OP will be anything that is greater than 32.We see only option E is greater than 32 .So option E

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vicky2019
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Re: What are the lengths of sides NO and OP in triangle NOP below? [#permalink] New post   12 Jul 2019, 22:22
Bunuel wrote:
What is the length of side OP in triangle NOP below?


A. 10
B. 30
C. \(\sqrt{34}\)
D. \(5\sqrt{34}\)
E. \(10\sqrt{34}\)

Show Spoiler
Attachment:
#GREexcecise What are the lengths of sides NO and OP in triangle NOP below.jpg


For this problem we can directly use options to answer.

one of the sides is 50 in a right angled triangle, so the the hypotenuse is definitely more than 50.

\sqrt{34} is almost equal to 6. Only option E gives value more than 50.

This procedure works only for this problem, because the options are scattered in that way.

Hope it helps.....!!
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Re: What are the lengths of sides NO and OP in triangle NOP below? [#permalink]
12 Jul 2019, 22:22
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