No. what you said is not possible just because of the constraint is the two line are parallel.

therefore,

Also, since AC || BD, we know that ∆WYX and ∆WZX have the SAME HEIGHT

as greenlight pointed already out.

Hope this helps.

Regards

Answer: C
The area of triangle WYX = 1/2 * H * WX
The area of triangle ZWX = 1/2 * H * WX

H is same for both of triangles because it is said that AC and BD are parallel and so all lines which crosse them in 90degrees, are equal.
A and B are equal and the answer is C.

Thank you.

Apologies for still asking a dumb question, but what is stopping the diagram from actually being something like this:

It's possible that the diagram looks like that.
However, if you add the lines that create triangles WYX and WZX, you'll find that those two triangles have the same base and height, which means their areas must be equal.

Cheers,
Brent

Thanks Brent!

Great view.

I think zizzi may have been confusing the length of the side of a triangle with it's height (which I imagine is a common mistake). The lengths of the sides of the triangle's in question are indeed different, but the length of the side of a triangle is not what is used in calculating the area of a triangle. The area of a triangle is calculated using the base and height. The base of the two triangles in this case is obviously the same. That the height is the same for both triangles may not be immediately obvious. If one draws out lines from the vertex opposite the base and perpendicular to the base for each triangle then I think that everyone will see that they are the same.

A hint that may help people remember that the side of a triangle is not necessarily the same as it's height is if one thinks of a tent. No one would confuse the length of the side of the tent with it's height. The height is from the base to the vertex opposite the base. (Triangle WZX resembles such a tent). If you were ordering a tent that you wanted to be able to stand up in, you wouldn't care about the length of the sides of the tent. You just want to know the height from the base of the tent, to the vertex opposite the base. As for a slanted triangle one could think of the Montreal Tower. The height of the tower is obviously not the same as the length of the side of the tower.

That's is a GREAT live example

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