D01-34

Look at the diagram below:Notice that no matter where point B is (blue or green dot) the area of the triangle would be the same, because the base (red segment) and the height would be the same.

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If vertices of a triangle are A (5, 0), B (x, y) and C (25, 0), what is the area of the triangle?


(1) |x| = y = 10

(2) x = |y| = 10

Given that vertices of a triangle are A (5, 0) and C (25, 0) =>Two vertices of the triangle are on x-axis =>Base = 20.
Area of a triangle = 1/2*(base)*(height)
Since, base is given, area of the triangle can be found if any of the following statement uniquely provide height of the triangle.

Statement 1:
|x| = y = 10
Or, x point lies on the line y=10 => height of the triangle=10 => sufficient.....(B)(C)(E)
Statement 2:
x = |y| = 10
Or, y point lies on the line x=10 => height of the triangle =10 => sufficient.....(A)(D)

Answer: (D)

Official Solution:


If vertices of a triangle are A (5, 0), B (x, y) and C (25, 0), what is the area of the triangle?

Statement 1: If \(|x| = y = 10\), \(y\) is 10 but \(x\) could be -10 or 10. The area is same for \(x = 10\) and \(x = -10\). This is sufficient to answer the question.

Statement 2: If \(x = |y| = 10\), \(x = 10\) but \(y\) could be 10 or -10 but different value of \(y\) does not affect the area of the triangle. This statement is also sufficient to answer the question.


Answer: D
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Can you please explain statement one in more detail i.e. how area is same .

Dear Bunuel,

Please correct me, if my reasoning for the above question is wrong.

The two specified co-ordinates will be on X-Axis.
(1) Y = 10 and the co-ordinate of x can be either 10 or -10, but in both the cases, X will lie on a straight line that is parallel to X Axis, thus we can use the Triangle area concept that if two points of a triangle lie on a line then the all the triangles formed with the third point on the parallel line will have the same area.

(2) The same concept can be used here. Though in this case, it is visible that the two triangles formed will be mirror image of each other, thus even in this case the area can be known.

Thus Answer should be D

Dear Bunuel, that is the same what i am draw and that is what i am ask for. In the green triangle I need to

understand which side is the height and how it equal to 10.I really confused

I think that you really need to brush up fundamentals on geometry.

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I think this is a high-quality question and I agree with explanation. loved the concept!!

I think this is a high-quality question. loved it.

I think this is a high-quality question and the explanation isn't clear enough, please elaborate. It is not clear in the explanation why the area is the same

I think this is a high-quality question and I agree with explanation.

The graph did everything. I am so mad I missed this question now.

I think this is a high-quality question and I agree with explanation. I don't think this is a 700 question..
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