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

Question

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

adalfu · Accepted Answer

i was so sure it was D until i saw the answer sheet... made me doubt myself there...

then i had to google: area of triangle, and stumbled upon this:
https://www.mathopenref.com/trianglearea.html

doesn't matter what the x coordinate is... as long as your base is fixed, and your height is fixed, area should be the same... but i still have to see it (and drag the coordinates around -- see link above) myself to believe it!!

h2polo · Answer

I agree that the answer is D as well. I spent a lot of time trying to figure this one out.

In short if you assume that two points at (5,0) and (25,0) are the base (which equals 20), you still get the same area regardless of whether the third point is at:

(10,10)
(-10,10)
(10,-10)
(-10,-10)

All that matters is that the height is still 10, because the area of a triange is 1/2*base*height: 1/2*10*20 = 100

flyingbunny · Answer

Answer should be C.

1) B can be two points B1(10, 10) or B2(-10,10)
therefore Sabc is not certain

2) B can be B1(10, 10) or B2(10, -10)
although AC is certain, but the height from B1 to AC and B2 to AC are not the same.
therefore Sabc is not certain

put 1) and 2) together, 
B can only be (10, 10)
Sabc can be calculated.

craky · Answer

The answer is D, both pairs of triangles have the same base and height.

Spidy001 · Answer

Area = 1/2 * base *height = 1/2*20*h

where h is the length of the perpendicular from (x,y) to x axis.

1. Sufficient

x>=0
=> x=y=10 => (x,y) = (10,10)
x<0
=> -x =y=10 =>(x,y) = (-10,10)

both of the above points result in the height of 10

2. Sufficient

y>=0

x=y=10 => (x,y) = (10,10)

y<0
x=-y=10 => (x,y) = (10,-10)

both of the above points result in the height of 10

Answer is D.

Bunuel · Answer

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 
 
The above statement means that  y  is 10, but  x  can be either -10 or 10. Thus, the third vertex B can be either at (-10, 10) or (10, 10). Notice, however, that the area will be the same in either case. The base of the triangle, the red segment in the image below, will have a length of 20, and the height from B will be 10. Therefore, the area of the triangle will be  \frac{1}{2}*20*10 = 100 . Sufficient.
 
 https://gmatclub.com/gmat-practice-tests/resources/import/img/D01-34-1+.png 
 
(2)  x = |y| = 10 
 
The above statement means that  x  is 10, but  y  can be either -10 or 10. Thus, the third vertex B can be either at (10, 10) or (10, -10). Notice, however, that the area will be the same in either case. The base of the triangle, the red segment in the image below, will have a length of 20, and the height from B will be 10. Therefore, the area of the triangle will be  \frac{1}{2}*20*10 = 100 . Sufficient.
 
 https://gmatclub.com/gmat-practice-tests/resources/import/img/D01-34-2.png

Answer: D

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

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

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