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

It is currently 21 Oct 2019, 18:11

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

The hypotenuse of a right triangle is 16 ft longer than the length of

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

Hide Tags

Find Similar Topics 
Intern
Intern
User avatar
S
Joined: 29 Dec 2018
Posts: 31
The hypotenuse of a right triangle is 16 ft longer than the length of  [#permalink]

Show Tags

New post 07 Mar 2019, 00:24
2
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

61% (02:55) correct 39% (03:22) wrong based on 33 sessions

HideShow timer Statistics

The hypotenuse of a right triangle is 16 ft longer than the length of the shorter leg. If the area of this triangle is exactly 120 ft², what is the length of the hypotenuse in feet?

A. 26

B. 32

C. 40

D. 64

E. 80
Math Expert
avatar
V
Joined: 02 Aug 2009
Posts: 8005
Re: The hypotenuse of a right triangle is 16 ft longer than the length of  [#permalink]

Show Tags

New post 07 Mar 2019, 01:25
MartinTao wrote:
The hypotenuse of a right triangle is 16 ft longer than the length of the shorter leg. If the area of this triangle is exactly 120 ft², what is the length of the hypotenuse in feet?

A. 26

B. 32

C. 40

D. 64

E. 80



Two ways..
(1) I would recommend use of choices as a priority in such a question.
Let the hypotenuse be option A, that is 26, so one leg = 26-16=10....
So the other side = \(\sqrt{26^2-10^2}=24\)
Thus, the area = (24*10)/2=120... TRUE
so answer A

(2) Algebraic method
Let the legs be x and y, so hypotenuse = x+16 and area xy/2=120 or xy=240
by Pythagorean theorem \((x+16)^2=x^2+y^2.....x^2+32x+256=x62+y^2.......y^2=32x+256\) substitute x= 240/y from xy=240
Thus, \(y^2=32*\frac{240}{y}+256.......y^3-256y=32*240\)
We are not asked cubic functions, that is power of 3, but we can use \(y(y^2-256)=32*240.......(y-16)(y+16)y=32*240=8*24*40=(24-16)*24*(24+16)\)
so y = 24, x= 240/24=10 and hypotenuse = \(\sqrt{24^2+10^2}=26\)

A
_________________
Intern
Intern
avatar
B
Joined: 11 Oct 2018
Posts: 21
Location: Germany
The hypotenuse of a right triangle is 16 ft longer than the length of  [#permalink]

Show Tags

New post 11 Mar 2019, 06:46
MartinTao wrote:
The hypotenuse of a right triangle is 16 ft longer than the length of the shorter leg. If the area of this triangle is exactly 120 ft², what is the length of the hypotenuse in feet?

A. 26

B. 32

C. 40

D. 64

E. 80


Another way is working with triangle properties.
We know that the sum of two sides must be greater than the third side. Let's work with this:

short leg: a
long leg: b
hypotenuse: c=a+16

This means, the long leg has to be longer than 16 ft.

Now, we factorize 240 (which is a*b).
\(240=2^4*3*5\)
\(2^4\) is \(16\), but we need greater than \(16\), so lets try \(2^3*3=24=b\).
In this case \(a=10, b=24, c=26\).

\(a+b>c...10+24=34>26\)
\(a+c>b...10+26=36>24\)
\(b+c>a...24+26=50>10\)

Answer (A)
GMAT Club Bot
The hypotenuse of a right triangle is 16 ft longer than the length of   [#permalink] 11 Mar 2019, 06:46
Display posts from previous: Sort by

The hypotenuse of a right triangle is 16 ft longer than the length of

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





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