Ans: d. 2:5

Using variables

In the given figure, we draw QT || VW.

$\Delta$ PTQ and $\Delta$ PVS are congruent (A,A,A and side)

Hence PT=Y, QT=X=UT (also since $\Delta$UTQ and $\Delta$UVW are similar).

Thus UV=UW=2X+Y. Area of square: $X^2+Y^2$; Area of  $\Delta$UVW= $\frac{1}{2}$ *(2X+Y)${}^2$.

Given X=2Y, $X^2+Y^2$: ( $\frac{1}{2}$ *(2X+Y)${}^2$) = 5Y${}^2$: ( 25Y${}^2$* $\frac{1}{2}$ ); = $\frac{2}{5}$.

 Using numbers,You can solve the problem faster as follows:

PV=2, SV=1 => PS= $\sqrt{5}$ $\Rightarrow$ Area of square =5

PTQ congruent to PVS

PT=1 and QT=2

UT=TQ (45-45-90) $\Rightarrow$ UT= 2

Now UV= 5 $\Rightarrow$ WV=5 (45-45-90)

UW=5$\sqrt{2}$