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

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

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

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.

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.



(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.




Answer: D