The correct answer is: Hence proved

Aim  :- Prove that 
Explanation(proof ) :-
Draw perpendicular to both sides of the rectangle .
We know EF is perpendicular to both AB and DC
It forms two new rectangles
So we get AE = DF (opposite sides of rectangle AEFD)
EB = FC (opposite sides of rectangle BCFE)

Using pythagoras theorem in triangle ARE
                            —-Eq1
Using pythagoras theorem in triangle BRE
                              —-Eq2
Using pythagoras theorem in triangle CRF
                              —-Eq3
Using pythagoras theorem in triangle ARE
                              —-Eq4
Doing Eq1 + Eq3 - (Eq2 +Eq4)
We get ,

Substitute  AE = DF ;EB = FC we get 
Therefore , 
Hence proved