Answer:
Answer A
Step-by-step explanation:
The Pythagorean formula in the small triangle gives
x² = w² + y²
x = √( w² + y² )
By this answer alone, answer C √( w * y ) is defenately false, because w*y is not w² + y², and therefore this answer can be discarded.
Answer B is also defenately wrong because the area indicated by the square on side z is much bigger then the area indicated by the square on side x.
Supose answer D is right, then
w*z must be equal to w² + y².
But from the big triangle we know that
v² = y² + z² , so y² = v² - z²
Since w*z is not v² - z², answer D must be wrong also.
The only answer which we can choose from is answer A, which must be the right answer since it is the only possibility left...
EXTRA
We have already deduced that answer A must be the right one, so we have already finished this question.
How ever, if answer A is right, then x = √( w(w + z) )
x = √( w² + wz )
From Pythagoras we know the next line to be true:
x = √( w² + y² )
From this, w*w = w² , no problem there, but then w*z must be equal to y². This is a problem for me at least...
At this moment I am unable to prove that w*z = y² but this seems at least plausible...
I leave it for now.
