What is the area of four sided figure formed by the intersection of

Question

What is the area of four sided figure formed by the intersection of the set of lines represented by |2x| + |y| = 6?

A. 18
B. 24
C. 30
D. 36
E. 48

Bunuel · Accepted Answer

LogicGuru1 · Answer

we just need four XY pair to define the four-sided figure. 
Lets works with the concept of X and Y intercepts 
When |x|=0; then |y|=6 .. right 
y=-6 and 6 ; XY pairs are {0,-6} and {0,6}

when |y|=0 then |2x|= 6
x=-3 and 3 ; The XY pairs are (-3,0 and 3,0)

When you plot these XY pairs you will see that you get a diamond shaped figure (an upright RHOMBUS ) which can be divided into 2 equal triangles. the base of these two triangles is the x-axis

Now area of a triangle = 1/2 * base * height = 1/2 * 6*6 (the distance between -3 and 3 is 6) and the height is 6-0 = 6
Therefore Area of the triangle =  \frac{1}{2}*36  =====>18 
There are 2 such triangle 
Total area = 2*18 =36
ANSWER IS D

shelrod007 · Answer

We need to find the equation |2X| + |Y| = 6

Equation 1 : 2X + Y = 6 which is Y = -2X + 6 . Points where this lines intersects the X and Y axis ( X = 0 , Y = 6 ) , ( X = 3 , Y = 0 )
 Equation 2 : -2X - Y = 6 which is Y = -2X - 6 . Points where this lines intersects the X and Y axis ( X = 0 , Y = -6 ) , ( X = -3 , Y = 0 )

From here we know the intersects of the lines , 
 Using area of triangles = 0.5 * X * Y 
 = 0.5 * 3 * 6 
 = 9 
 Using symmetry 4 triangles = 9 * 4 
 = 36 . 
 Answer is D . ( Sketch a diagram to visualize it helps !! )

Midori2016 · Answer

Is it correct if I assume that the area is the product of the following two equations?

2x+y=6
2x+y=-6

prady80 · Answer

These are four equations. If you carefully observe these equations because of the way mod functions are plotted around y and x axis as opposite images, these four lines form a rhombus with diagonals of lengths as 6 and 12 (if x =0 then possible y values 0,6 and 0,-6) and then (if y =0 x intercepts at 3,0 and -3,0. Area of rhombus is 1/2 * (product of diagonals) = 1/2 * 12 *6 = 36.

ameyaprabhu · Answer

What's the fastest way to solve this?

I took almost 4 mins. First opened mods and found the 4 equations. Then found 2 points per equation. Then found area of one triangle and multiplied it by 4 (for area of the 4 triangles formed)

mvictor · Answer

took me some time to draw some points...
but i believe the easiest way is:
x=0, then y=6 or -6.
y=0, x=3 or -3.
we get 4 similar 90 degrees triangles, with the 90 degree angle at the origin.
short leg is 3, long leg is 6.
area is leg*leg/2 = 18/2 = 9.
since we have 4 of these triangles, the area is 9*4 = 36.

D

Madhavi1990 · Answer

Can someone give a diagrammatic answer to this? Would be really helpful to understand what kind of rhombus or square gets created :)

Rishovnits · Answer

Please correct me if i am wrong.

|2x|+|y|=6

When, x=2, y=2,-2 Points are (2,2) and (2,-2)
When, x=-2 y=2,-2 Points are (-2,2) and (-2,-2)

I get a square with an area of (4x4) =16.

Bunuel · Answer

It's a rhombus. Check here: https://gmatclub.com/forum/what-is-the- ... l#p1910705

Shobhit7 · Answer

From the equation, we know that for all the four lines: 
y-intercept is either +6 or -6
& 
x-intercept is either +3 or -3

So, the shape of the quadrilateral is a rhombus with one diagnol length as 12 (from +6 to -6) and other diagnol length as 6 (from +3 to -3)

Therefore, Area of Rhombus= (d1xd2)/2 = (12x6)/2 = 36.

Ans D.

Posted from my mobile device

AweG · Answer

By drawing a diagram we see that we have a rhombus .We know that each side of the rhombus is X so  Area=base*hight=x^2  must be a perfect square of a number D.  36=6^2  fits

mangotango12334 · Answer

Can't (1,4) (-1,4) 
 (2,2), (-2,-2) be used to solve the problem? Maybe I didn't understand the question properly...

thekingslay · Answer

Please remove this if found irrelevant-->

I solved this in 17 seconds. My logic - it has 2, 1 on LHS and 6 on RHS. 36 has all of these. (2+1) and (6). So I clicked C with confidence.

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What is the area of four sided figure formed by the intersection of

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