What expression represents the value of y?

The expression which represent the value of y is    ( option b )

Step-by-step explanation:

Given as figure :

Right angle Triangle BDC   with right angle at D having

BD = y

DC = w

CB = x

And Triangle CBA with right angle at B having

BA = v

AC = AD + DC = z + w

CB = x

Now from Δ BDC

Pythagoras Theorem

BC² = CD² + DB²

Or, x² = w² + y²  ...1  

From  Δ CBA

AC² = CB² + BA²

Or, ( z + w )² = x² + v²

Or,  z² + w² + 2 z w = x² + v²     ...2

From  Δ BDA

AB² = BD² + DA²

Or, v² = y² + z²    ....3

From eq 1 and eq 2

z² + w² + 2 z w = w² + y² + v²  

Or, z² +  (w² -  w² ) + 2 z w = y² + v²  

Or, z² + 2 z w = y² + v²  

Or, eq  

z² + 2 z w = y² +  y² + z²

Or.  z²  -  z²  + 2 z w = 2 y²

Or,  2 z w = 2 y²

∴  y² = zw

I,e y =  

Hence The expression which represent the value of y is    ( option b )    Answer