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Point X lies on side BC of rectangle ABCD, which has length 12 and wid

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Bunuel
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Point X lies on side BC of rectangle ABCD, which has length 12 and wid [#permalink] New post  30 Jul 2018, 01:22
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Point X lies on side BC of rectangle ABCD, which has length 12 and width 8. What is the area of triangular region AXD ?

A. 96
B. 48
C. 32
D. 24
E. 20


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(PS09983)
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ScottTargetTestPrep
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Re: Point X lies on side BC of rectangle ABCD, which has length 12 and wid [#permalink] New post  10 Aug 2018, 18:50
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Bunuel wrote:
Point X lies on side BC of rectangle ABCD, which has length 12 and width 8. What is the area of triangular region AXD ?

A. 96
B. 48
C. 32
D. 24
E. 20


When a triangle is formed by connecting a point on a side of the rectangle and the endpoints of the opposite side of the rectangle, such a triangle will have an area that is half of the area the rectangle. Since rectangle ABCD has an area of 12 x 8 = 96, triangle AXD will have an area of ½(96) = 48.

Answer: B
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chetan2u
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Re: Point X lies on side BC of rectangle ABCD, which has length 12 and wid [#permalink] New post  30 Jul 2018, 01:44
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Bunuel wrote:
Point X lies on side BC of rectangle ABCD, which has length 12 and width 8. What is the area of triangular region AXD ?

A. 96
B. 48
C. 32
D. 24
E. 20


NEW question from GMAT® Quantitative Review 2019


(PS09983)



irrespective what is length or breadth ans will be same..
if BC is 8, height is 12 and area = \(\frac{1}{2}*8*12=48\)
If BC is 12, height is 8 and area = \(\frac{1}{2}*8*12=48\)

B
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sudarshan22
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Re: Point X lies on side BC of rectangle ABCD, which has length 12 and wid [#permalink] New post  30 Jul 2018, 04:25
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Bunuel wrote:
Point X lies on side BC of rectangle ABCD, which has length 12 and width 8. What is the area of triangular region AXD ?


+1 for B.

Area of rectangle ABCD = L * W = 12 * 8 = 96

Since Point X lies on side BC of rectangle, therefore Base of the triangle AD = 12, and Height of the triangle AB = 8

Area of the triangle = 1/2 * B * H = 1/2 * 12 * 8 = 48

Hence, B.
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ironsheep
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Re: Point X lies on side BC of rectangle ABCD, which has length 12 and wid [#permalink] New post  22 Jul 2019, 22:36
I still don't get this problem. You assume that any triangle inside a rectangle is already (1/2) the area of the rectangle. I know the base of the triangle is 8, but i can't find out how to find the height of that triangle.
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Bunuel
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Re: Point X lies on side BC of rectangle ABCD, which has length 12 and wid [#permalink] New post  23 Jul 2019, 23:07
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ironsheep wrote:
I still don't get this problem. You assume that any triangle inside a rectangle is already (1/2) the area of the rectangle. I know the base of the triangle is 8, but i can't find out how to find the height of that triangle.


Height = 12 and base = 8 or vise-versa. You can check the diagrams here: https://gmatclub.com/forum/point-x-lies ... l#p2103641
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Re: Point X lies on side BC of rectangle ABCD, which has length 12 and wid [#permalink] New post  25 Jul 2019, 03:14
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Solution



Given:
    • Point X lies on side BC of rectangle ABCD.
    • Length of rectangle ABCD is 12 and width is 18.

To find:
    • Area of triangular region AXD.

Approach and Working

Area of triangle = ½ × Base × Height
    • = ½ × Length of rectangle × width of rectangle
    • = ½ ×12 × 8= 48
Hence, the correct answer is B.
Correct answer: Option B
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Re: Point X lies on side BC of rectangle ABCD, which has length 12 and wid [#permalink] New post  18 Aug 2019, 04:37
EgmatQuantExpert wrote:

Solution



Given:
    • Point X lies on side BC of rectangle ABCD.
    • Length of rectangle ABCD is 12 and width is 18.

To find:
    • Area of triangular region AXD.

Approach and Working

Area of triangle = ½ × Base × Height
    • = ½ × Length of rectangle × width of rectangle
    • = ½ ×12 × 8= 48
Hence, the correct answer is B.
Correct answer: Option B




Hi Egmat,

I don’t understand how the length and breadth of the triangle would be the same as rectangle. If X is a point on BC, then area of ABX= 1/2* 12* length of BX (Assuming BC is the breadth and AB is the length of rectangle)

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Re: Point X lies on side BC of rectangle ABCD, which has length 12 and wid [#permalink] New post  06 Nov 2020, 07:19
Point X lies on side BC of rectangle ABCD, which has length 12 and width 8. What is the area of triangular region AXD ?

\(\frac{12 * 8 }{ 2} = 48\)

The triangle is half the area of the rectangle. AXD = 48.
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Re: Point X lies on side BC of rectangle ABCD, which has length 12 and wid [#permalink] New post  15 Jan 2021, 16:29
Hi all, something that got me confused in this question...How do you know where point X lies on line BC? It does not say that point X is midway on line BC and therefore this could impact the total area? Please could someone help me understand if I am doing something wrong.

Thank you!
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Re: Point X lies on side BC of rectangle ABCD, which has length 12 and wid [#permalink] New post  21 Feb 2021, 19:46
clover1987 wrote:
Hi all, something that got me confused in this question...How do you know where point X lies on line BC? It does not say that point X is midway on line BC and therefore this could impact the total area? Please could someone help me understand if I am doing something wrong.

Thank you!


I got the same initial confusion, ultimately where point X line on BC does not matter, because the height of triangle AXD will always be equal to AB/CD (since it measures the distance of a point in BC to AD so that XH is perpendicular to AD) and the base = AD, so the area of the triangle is AB*AD/2 which is half of the area of the rectangular (AB*AD) :please:
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prathyushetty10
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Re: Point X lies on side BC of rectangle ABCD, which has length 12 and wid [#permalink] New post  04 Dec 2021, 03:53
Area of a right angle triangle is 1/2 x b x h. Based on what criterion have you all assumed that it is a right angled triangle ?Bunuel
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