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# In the rectangular coordinate system above, what is the area of triang

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In the rectangular coordinate system above, what is the area of triang  [#permalink]

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23 Sep 2019, 00:00
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In the rectangular coordinate system above, what is the area of triangular region AED?

(1) The area of region ABCD is 12.

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Re: In the rectangular coordinate system above, what is the area of triang  [#permalink]

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23 Sep 2019, 00:13
1
We are to determine the area of triangle AED

From the figure area of triangle
AED= 1/2 * (3k)(2k) = 3k^2
So we need to know the value of k or somehow figure out what is 3k^2

Statement 1 alone is sufficient.
We are given in statement 1 that Rectangle ABCD=12
But from the figure area of ABCD=k(3k)=3k^2 which is the same as area of AED.
Hence we can say that AED has an area =12.

Statement 2 is also sufficient.
We are given in 2 that AD=3k=6 meaning k=2

Since we know k, we can determine area AED=3*2^2 = 12.

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Re: In the rectangular coordinate system above, what is the area of triang  [#permalink]

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23 Sep 2019, 00:16
1
the area of triangular region AED = 2k*3k

(1) The area of region ABCD is 12.....from this we can k value as 2.....so sufff
2) AD = 6 ......from we can also get 6k=12, k=2......suffff

SO OA:D
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Re: In the rectangular coordinate system above, what is the area of triang  [#permalink]

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23 Sep 2019, 00:17
1
Seeing figure we can determine thaat AD= 3k and AB is K
given area ABCD = 12
3k^2 = 12
k=2
#1 is sufficient
as by using distance formula we can find sides of ∆AED
#2
3k=6
k=2
sufficient
IMO D

In the rectangular coordinate system above, what is the area of triangular region AED?

(1) The area of region ABCD is 12.
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Re: In the rectangular coordinate system above, what is the area of triang  [#permalink]

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23 Sep 2019, 00:57
1
(1) The area of region ABCD is 12.
we know that the area of the triangle is the same if the base and height are the same.
we have an area of ABCD which is 12 so the area above portion will also be 12.
The area of a rectangular will be 24 and the area of the triangle will be half of rectangle i.e. 12.
Sufficient.

AD is 6 i.e. 4k - k = 6
k=2
We can identify height
h=4
area of triangle = 1/2*4*6 = 12
Sufficient

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Re: In the rectangular coordinate system above, what is the area of triang  [#permalink]

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23 Sep 2019, 03:05
Quote:

In the rectangular coordinate system above, what is the area of triangular region AED?

(1) The area of region ABCD is 12.

(1) The area of region ABCD is 12: $$3k(k)=12…k^2=4…k=2$$, sufic.
(2) AD = 6; $$AD=3k=6…k=2$$, sufic.

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Re: In the rectangular coordinate system above, what is the area of triang  [#permalink]

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23 Sep 2019, 03:18
Let point(k,6k) in the coordinate system is called point F.

Area of Δ AED = Area of ΔAEF - Area of ΔDEF
 $$= \frac{1}{2} * AF * EF – 1/2 * AF * DF$$
 $$= \frac{1}{2} * EF *(AF – DF)$$
 $$= \frac{1}{2} * (3k - k) * (6k – k – (4k – k))$$
 $$= \frac{1}{2} * 2k * 2k$$
 $$= \frac{1}{2} * 4k^2$$
So, k = ?

(1) The area of region ABCD is 12.

Area of region ABCD = AB * AD
 = (2k - k) * (4k - k)
 = 3k*k
 3k*k = 12
 K = 2

SUFFICIENT.

AD = 4k – k = 3k
 3k = 6
 K = 2

SUFFICIENT.

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Re: In the rectangular coordinate system above, what is the area of triang  [#permalink]

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23 Sep 2019, 08:04
to find area of the triangle = height X base AD/2= (2k X 3K )/2= 3k^2

1)sufficient : we are given AD x k = 3k^2 =12
2)sufficient AD=3k given so we can find 3k^2
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Re: In the rectangular coordinate system above, what is the area of triang  [#permalink]

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23 Sep 2019, 16:26
In the coordinate system,
The area of triangle of AED = $$\frac{5k*2k}{2}-\frac{2k*2k}{2}$$=$$5k^{2}-2k^{2}$$=$$3k^{2}$$ ???

Statement1: ABCD is a rectangle --> k*3k=12 --> k=2
--> $$3k^{2}$$=12
Sufficient

k=2
The same result as Statement1
Sufficient

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Re: In the rectangular coordinate system above, what is the area of triang  [#permalink]

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14 Nov 2019, 05:42
Hi guys, a rather silly question that I had..

From (1) we find k=2 and with this we can find all the co-ordinates of the triangle. With distance formula we can find the lengths of each side of triangle. But since area of triangle is bh/2, how do we know which is side is the height and which is the base?

Thanks.
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Re: In the rectangular coordinate system above, what is the area of triang  [#permalink]

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14 Nov 2019, 07:33
mokiburnsred wrote:
Hi guys, a rather silly question that I had..

From (1) we find k=2 and with this we can find all the co-ordinates of the triangle. With distance formula we can find the lengths of each side of triangle. But since area of triangle is bh/2, how do we know which is side is the height and which is the base?

Thanks.

every side of the triangle can be treated as base we are treating the bottom side as base as it coincides with the rectangle and we can find its value easily
Re: In the rectangular coordinate system above, what is the area of triang   [#permalink] 14 Nov 2019, 07:33
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