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What is the length of hypotenuse k?

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What is the length of hypotenuse k? [#permalink]

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New post 27 Oct 2014, 20:14
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A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

65% (02:54) correct 35% (02:51) wrong based on 97 sessions

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File comment: ans is 7.8
1b.jpg
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What is the length of hypotenuse k?

(A) 7.8
(B) 9
(C) 6.9
(D) 6.8
(E) 7
[Reveal] Spoiler: OA

Last edited by Bunuel on 28 Oct 2014, 02:40, edited 1 time in total.
Renamed the topic and edited the question.

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Re: What is the length of hypotenuse k? [#permalink]

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New post 28 Oct 2014, 00:22
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anik89 wrote:
a. 7.8
b.4.8
c. 10.8
d.6.5


This diagram shown is not as per the values obtained. I'm posting the corrected one.......
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1b.jpg
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Re: What is the length of hypotenuse k? [#permalink]

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New post 28 Oct 2014, 01:28
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PareshGmat wrote:
anik89 wrote:
a. 7.8
b.4.8
c. 10.8
d.6.5


This diagram shown is not as per the values obtained. I'm posting the corrected one.......


Because:
A1 + A2 = 90 degrees;
B + A1 = 90 degrees
A2 + C = 90 degree

==> A2 = B & A1 = C
The two right triangles are similar

==> \(12/ 7.2 = 13/k\)
==> \(k = (7.2*13)/12 > (7.2*12)/12 = 7.2\)
==>\(k = 7.8\)

A is the answer.
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Re: What is the length of hypotenuse k? [#permalink]

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Refer diagram below & angles given

Attachment:
1b.jpg
1b.jpg [ 20.43 KiB | Viewed 2011 times ]


\(\triangle\) ABC is similar to \(\triangle\) CDE

So, corresponding sides are also similar

\(\frac{12}{7.2} = \frac{13}{k}\)

\(k = 13 * \frac{7.2}{12} = 7.8\)

Answer = A
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Re: What is the length of hypotenuse k? [#permalink]

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New post 24 Nov 2014, 13:50
can you please explain how triangle ABC is similar to triangle CDE


PareshGmat wrote:
Refer diagram below & angles given

Attachment:
1b.jpg


\(\triangle\) ABC is similar to \(\triangle\) CDE

So, corresponding sides are also similar

\(\frac{12}{7.2} = \frac{13}{k}\)

\(k = 13 * \frac{7.2}{12} = 7.8\)

Answer = A

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Re: What is the length of hypotenuse k? [#permalink]

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New post 24 Nov 2014, 20:02
sunita123 wrote:
can you please explain how triangle ABC is similar to triangle CDE


PareshGmat wrote:
Refer diagram below & angles given

Attachment:
1b.jpg


\(\triangle\) ABC is similar to \(\triangle\) CDE

So, corresponding sides are also similar

\(\frac{12}{7.2} = \frac{13}{k}\)

\(k = 13 * \frac{7.2}{12} = 7.8\)

Answer = A



The corresponding angles are equal (refer earlier posts, angles are calculated in "red") so the triangles are similar

Visualize rotating both the triangles such that sides CD & CE are bases of the triangle. It would be helpful.

Once its determined that angles are same, then we can calculate the corresponding dimensions as shown
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Re: What is the length of hypotenuse k? [#permalink]

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Re: What is the length of hypotenuse k? [#permalink]

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New post 11 Apr 2017, 19:28
My approach:

13^2 = 12^2 + x ^2
169 = 144 + x^2
x = 5

12.2 - 5 = 7.2

k^2 = 5^2 + unknown ^ 2
k^2 = 25 + unknown ^ 2

Let's look at the answer choices and do process elimination
When you plug in the numbers for Pythagorean theorem, it can not be C, D and E since 7.2 ^ 2 = 51.84 and k^2 needs to be greater than 51.84

A x^2 = 7.8 ^2 - 51.84
60.84 - 51.84 = 9
x = 3

B 9 ^2 - 51.84
81 - 51.84 = 30.16
x^2 = 30.16
Won't result as an integer

Therefore, the answer is A

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Re: What is the length of hypotenuse k? [#permalink]

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New post 15 Sep 2017, 08:20
Clearly the answer is A
see the figure for explanation
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Re: What is the length of hypotenuse k?   [#permalink] 15 Sep 2017, 08:20
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