NEW HERE? LEARN MORE
closeclose
Last visit was: 25 Apr 2024, 06:31 It is currently 25 Apr 2024, 06:31
Decision Tracker
My Rewards
New posts
New comers' posts

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

What is the area of a triangle whose sides are formed by the x−axis

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92912
Own Kudos [?]: 618940 [0]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
What is the area of a triangle whose sides are formed by the x−axis [#permalink] New post   26 May 2018, 07:48
Expert Reply
00:00
A
B
C
D
E

Difficulty:

5% (low)

Question Stats:

83% (01:22) correct 17% (01:30) wrong based on 132 sessions
Hide Show timer Statistics
What is the area of a triangle whose sides are formed by the x−axis, the y−axis, and the line \(y = −\frac{3}{4}x + 9\)?

A. 6
B. 18
C. 36
D. 54
E. 72
ShowHide Answer
Official Answer
D
User avatar
L
u1983
Current Student
Joined: 24 Aug 2016
Posts: 733
Own Kudos [?]: 772 [2]
Given Kudos: 97
GMAT 1: 540 Q49 V16
GMAT 2: 680 Q49 V33
Send PM
GMAT ToolKit User Reviews Badge
Re: What is the area of a triangle whose sides are formed by the x−axis [#permalink] New post   26 May 2018, 08:34
2
Kudos
Bunuel wrote:
What is the area of a triangle whose sides are formed by the x−axis, the y−axis, and the line \(y = −\frac{3}{4}x + 9\)?

A. 6
B. 18
C. 36
D. 54
E. 72


For a triangle whose sides are formed by the x−axis, the y−axis , we can consider the distance between origin (0,0) & the triangle's vertex of the y-axis to be height & the distance between origin (0,0) & the triangle's vertex of the x-axis vertex to be base of the triangle. These two are y-intercept & x intercept of the given line.
y intercept : when x=0, \(y = −\frac{3}{4}*0 + 9\) ==>\(y=9\)
x intercept : when y=0, \(0 = −\frac{3}{4} + 9\) ==> \(-9 = −\frac{3}{4}x\) ==>\(3 = \frac{1}{4}x\) ==>\(12 = x\)
Hence the area =\(\frac{1}{2} *12*9\) =\(54\)

Hence I would go for option D.
User avatar
S
anuj04
Manager
Manager
Joined: 25 Jul 2017
Posts: 68
Own Kudos [?]: 88 [2]
Given Kudos: 42
Send PM
Re: What is the area of a triangle whose sides are formed by the x−axis [#permalink] New post   26 May 2018, 08:47
2
Kudos
we just need to calclate the X & Y intercepts. This can be calculated by putting X=0 & Y=0, one by one in the equation of the third side of the triangle.
1. when y=0 then -3/4X + 9=0 i.e. 3/4x=9. i.e x=12
2. when x=0 then -3/4*0 + 9=Y i.e. Y=9.
Now are of the triangle is 1/2bh => 1/2 * 12 * 9 = 54.

Answer is D.
avatar
P
Shobhit7
Manager
Manager
Joined: 01 Feb 2017
Posts: 246
Own Kudos [?]: 346 [0]
Given Kudos: 148
Send PM
Re: What is the area of a triangle whose sides are formed by the x−axis [#permalink] New post   26 May 2018, 12:22
Base of triangle on x-axis= x intercept= 12

Height of triangle on y-axis= y intercept= 9

Area of triangle= (9*12)/2= 54

Ans D

Posted from my mobile device
User avatar
P
SSM700plus
Manager
Manager
Joined: 01 Aug 2017
Posts: 167
Own Kudos [?]: 161 [1]
Given Kudos: 420
Location: India
Concentration: General Management, Leadership
Schools: ISB '20 (S) IIMA PGPX"20 (S)
GMAT 1: 500 Q47 V15
GPA: 3.4
WE:Information Technology (Computer Software)
Send PM
Reviews Badge
Re: What is the area of a triangle whose sides are formed by the x−axis [#permalink] New post   26 May 2018, 12:46
1
Kudos
Bunuel wrote:
What is the area of a triangle whose sides are formed by the x−axis, the y−axis, and the line \(y = −\frac{3}{4}x + 9\)?

A. 6
B. 18
C. 36
D. 54
E. 72


This is the equation of line. Let's change it to intercept form so that x and y intercepts can be calculated easily.
\(y = −\frac{3}{4}x + 9\)

\(y + \frac{3}{4}x = 9\)

\(\frac{y}{9} + \frac{3}{4.9}x = 1\).

\(\frac{y}{9} + \frac{x}{12} = 1\).

Now Line intersects the x axis at (12,0) and Y axis at (0,9).

If you could imagine a line passing thru these points (12,0) ,(0,9) ,x axis and y-axis.
Height & base of Triangle is 9 & 12. You can also consider vice-versa.

Area of Triangle = \(\frac{1}{2} * 12* 9 = \frac{108}{2}\)= 54.

Ans - D
GMAT Club Bot
gmatclubot
Re: What is the area of a triangle whose sides are formed by the x−axis [#permalink]
26 May 2018, 12:46
Moderators:
Bunuel
Math Expert
92912 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions