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

It is currently 26 Sep 2018, 05:56

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

In right triangle ABC, the ratio of the lengths of the two legs is 2

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49537
In right triangle ABC, the ratio of the lengths of the two legs is 2  [#permalink]

Show Tags

New post 13 Jul 2018, 00:43
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

95% (01:16) correct 5% (00:36) wrong based on 20 sessions

HideShow timer Statistics

In right triangle ABC, the ratio of the lengths of the two legs (non-hypotenuse sides) is 2 to 5. If the area of triangle ABC is 20, what is the length of the hypotenuse?


A. 7
B. 10
C. \(4 \sqrt{5}\)
D. \(\sqrt{29}\)
E. \(2 \sqrt{29}\)

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

SC Moderator
User avatar
G
Joined: 30 Jan 2015
Posts: 602
Location: India
Concentration: Operations, Marketing
GPA: 3.5
Re: In right triangle ABC, the ratio of the lengths of the two legs is 2  [#permalink]

Show Tags

New post 13 Jul 2018, 00:54
Bunuel wrote:
In right triangle ABC, the ratio of the lengths of the two legs (non-hypotenuse sides) is 2 to 5. If the area of triangle ABC is 20, what is the length of the hypotenuse?


Let the two legs of the right triangle ABC be 2x and 5x
Now, area = 1/2 * leg1 * leg2
20 = 1/2 * 2x * 5x
x = 2
Putting x's value in respective legs and by pythagoras theorem we can get the hypotenuse
h^2 = 4^2 + 10^2
h^2 = 116
h = 2 root 29

Hence, E.
_________________

The few, the fearless !

Thanks :-)

RC Moderator
User avatar
D
Status: Perfecting myself for GMAT
Joined: 22 May 2017
Posts: 650
Concentration: Nonprofit
Schools: Haas '21
GPA: 4
WE: Engineering (Computer Software)
Re: In right triangle ABC, the ratio of the lengths of the two legs is 2  [#permalink]

Show Tags

New post 13 Jul 2018, 00:55
In right triangle ABC, the ratio of the lengths of the two legs (non-hypotenuse sides) is 2 to 5

=> one leg is 2x and the other leg is 5x

=> These two legs form the base and height for the right triangle

=> Area = \(\frac{1}{2} * base * height = \frac{1}{2} * 2x * 5x = 20\)

=> \(5x^2 = 20\)

=> \(x^2 = 4\)

=> x = 2

The legs of right triangle are 2x = 4 and 5x = 10

length of the hypotenuse = \(\sqrt{(4)^2 + (10)^2}\)

=> \(\sqrt{16 + 100}\)

=> \(2\sqrt{29}\)

Hence option E
_________________

If you like my post press kudos +1

New - RC Butler - 2 RC's everyday

Tag me in RC questions if you need help. Please provide your analysis of the question in the post along with the tag.

Senior SC Moderator
avatar
V
Joined: 22 May 2016
Posts: 1984
Premium Member CAT Tests
In right triangle ABC, the ratio of the lengths of the two legs is 2  [#permalink]

Show Tags

New post 13 Jul 2018, 17:38
Bunuel wrote:
In right triangle ABC, the ratio of the lengths of the two legs (non-hypotenuse sides) is 2 to 5. If the area of triangle ABC is 20, what is the length of the hypotenuse?


A. 7
B. 10
C. \(4 \sqrt{5}\)
D. \(\sqrt{29}\)
E. \(2 \sqrt{29}\)

Ratio of legs with multiplier \(x\):
\(\frac{Leg_1}{Leg_1}=\frac{2x}{5x}\)
Area = \(\frac{b*h}{2}=\frac{2x*5x}{2}=20\)
\(5x^2=20\)
\((x^2=4) => x=2\)

Multiplier \(x=2\), so
\(Leg_1=2x=(2*2)=4\)
\(Leg_2=5x=(5*2)=10\)

Hypotenuse
\(4^2+10^2=h^2\)
\(\sqrt{h^2}=\sqrt{116}\)
\(\sqrt{h^2}=\sqrt{2*2*29}\)
\(h=2\sqrt{29}\)

Answer E
_________________

In the depths of winter, I finally learned
that within me there lay an invincible summer.

-- Albert Camus, "Return to Tipasa"

GMAT Club Bot
In right triangle ABC, the ratio of the lengths of the two legs is 2 &nbs [#permalink] 13 Jul 2018, 17:38
Display posts from previous: Sort by

In right triangle ABC, the ratio of the lengths of the two legs is 2

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  

Events & Promotions

PREV
NEXT


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.