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TAGS: GRE Instructor Joined: 10 Apr 2015
Posts: 1525
Followers: 55

Kudos [?]: 1455  , given: 8

What is the area of a triangle created by the intersections [#permalink]
1
KUDOS
Expert's post 00:00

Question Stats: 50% (01:12) correct 50% (01:18) wrong based on 2 sessions
What is the area of a triangle created by the intersections of the lines $$x=4$$, $$y=5$$ and $$y = -\frac{3}{4}x + 20$$?

A. 42
B. 54
C. 66
D. 72
E. 96
[Reveal] Spoiler: OA

_________________

Brent Hanneson – Creator of greenlighttestprep.com Sign up for our free GRE Question of the Day emails

Supreme Moderator
Joined: 01 Nov 2017
Posts: 370
Followers: 5

Kudos [?]: 107 , given: 4

Re: What is the area of a triangle created by the intersections [#permalink]
Expert's post
GreenlightTestPrep wrote:
What is the area of a triangle created by the intersections of the lines $$x=4$$, $$y=5$$ and $$y = -\frac{3}{4}x + 20$$?

A. 42
B. 54
C. 66
D. 72
E. 96

x=4 and y=5 are perpendicular lines so we have a right angled triangle at their intersection.

Now the height will be on x=4 and will be till $$y = -\frac{3}{4}x + 20$$ intersects it. So, when x=4, $$y = -\frac{3}{4}*4 + 20=17$$..
Height is Displacement in y coordinates = 17-5=12

Now the base will be on y=5 and will be till $$y = -\frac{3}{4}x + 20$$ intersects it. So, when y=5, $$5= -\frac{3}{4}*x + 20=17....5-20=\frac{-3}{4}x.....x=\frac{15*4}{3}=20$$..
Base is Displacement in x coordinates = 20-4=16..

Area = $$\frac{1}{2}*16*12=96$$

E
_________________

Some useful Theory.
1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
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4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html
5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html

GRE Instructor Joined: 10 Apr 2015
Posts: 1525
Followers: 55

Kudos [?]: 1455 , given: 8

Re: What is the area of a triangle created by the intersections [#permalink]
Expert's post
GreenlightTestPrep wrote:
What is the area of a triangle created by the intersections of the lines $$x=4$$, $$y=5$$ and $$y = -\frac{3}{4}x + 20$$?

A. 42
B. 54
C. 66
D. 72
E. 96

Let's first sketch the lines x = 4 and y = 5 To find the point where y = (-3/4)x + 20 intersects the line x = 4, replace x with 4 to get: y = (-3/4)4 + 20 = 17
So the point of intersection is (4, 17)

To find the point where y = (-3/4)x + 20 intersects the line y = 5, replace y with 5 to get: 5 = (-3/4)x + 20
When we solve for x, we get x = 20
So the point of intersection is (20, 5)

Add this information to our sketch: From here, we can determine the length of the right triangle's base and height: Area = (1/2)(base)(height)
= (1/2)(16)(12)
= 96

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com Sign up for our free GRE Question of the Day emails Re: What is the area of a triangle created by the intersections   [#permalink] 09 Jan 2019, 06:37
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