GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 19 Jun 2018, 16:38

### 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 is the length of hypotenuse k?

Author Message
TAGS:

### Hide Tags

Intern
Joined: 08 May 2014
Posts: 8
What is the length of hypotenuse k? [#permalink]

### Show Tags

Updated on: 28 Oct 2014, 02:40
1
5
00:00

Difficulty:

65% (hard)

Question Stats:

66% (02:56) correct 34% (02:49) wrong based on 108 sessions

### HideShow timer Statistics

Attachment:
File comment: ans is 7.8

1b.jpg [ 14.37 KiB | Viewed 2454 times ]
What is the length of hypotenuse k?

(A) 7.8
(B) 9
(C) 6.9
(D) 6.8
(E) 7

Originally posted by anik89 on 27 Oct 2014, 20:14.
Last edited by Bunuel on 28 Oct 2014, 02:40, edited 1 time in total.
Renamed the topic and edited the question.
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1837
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: What is the length of hypotenuse k? [#permalink]

### Show Tags

28 Oct 2014, 00:22
1
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.......
Attachments

1b.jpg [ 18.02 KiB | Viewed 2362 times ]

_________________

Kindly press "+1 Kudos" to appreciate

Retired Moderator
Joined: 16 Jun 2012
Posts: 1079
Location: United States
Re: What is the length of hypotenuse k? [#permalink]

### Show Tags

28 Oct 2014, 01:28
2
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

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

Attachments

1b.jpg [ 19.42 KiB | Viewed 2392 times ]

_________________

Please +1 KUDO if my post helps. Thank you.

"Designing cars consumes you; it has a hold on your spirit which is incredibly powerful. It's not something you can do part time, you have do it with all your heart and soul or you're going to get it wrong."

Chris Bangle - Former BMW Chief of Design.

SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1837
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: What is the length of hypotenuse k? [#permalink]

### Show Tags

28 Oct 2014, 03:15
1
1
Refer diagram below & angles given

Attachment:

1b.jpg [ 20.43 KiB | Viewed 2375 times ]

$$\triangle$$ ABC is similar to $$\triangle$$ CDE

So, corresponding sides are also similar

$$\frac{12}{7.2} = \frac{13}{k}$$

$$k = 13 * \frac{7.2}{12} = 7.8$$

_________________

Kindly press "+1 Kudos" to appreciate

Manager
Joined: 13 Oct 2013
Posts: 130
Concentration: Strategy, Entrepreneurship
Re: What is the length of hypotenuse k? [#permalink]

### Show Tags

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

$$\frac{12}{7.2} = \frac{13}{k}$$

$$k = 13 * \frac{7.2}{12} = 7.8$$

_________________

---------------------------------------------------------------------------------------------
Kindly press +1 Kudos if my post helped you in any way

SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1837
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: What is the length of hypotenuse k? [#permalink]

### Show Tags

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

$$\frac{12}{7.2} = \frac{13}{k}$$

$$k = 13 * \frac{7.2}{12} = 7.8$$

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
_________________

Kindly press "+1 Kudos" to appreciate

Senior Manager
Joined: 06 Dec 2016
Posts: 251
Re: What is the length of hypotenuse k? [#permalink]

### Show Tags

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

Director
Joined: 29 Jun 2017
Posts: 500
GPA: 4
WE: Engineering (Transportation)
Re: What is the length of hypotenuse k? [#permalink]

### Show Tags

15 Sep 2017, 08:20
see the figure for explanation
Attachments

IMG_0617.jpg [ 1.2 MiB | Viewed 526 times ]

_________________

Give Kudos for correct answer and/or if you like the solution.

Re: What is the length of hypotenuse k?   [#permalink] 15 Sep 2017, 08:20
Display posts from previous: Sort by