Let x and y be the dimensions of the rectangle.


2x + 2y = 92,   hence

 x + y = 46.               (1)


The second equation is

 = 34,   or

x^2 + y^2 = 34^2           (2)


Square both sides of eq(1). You will get


x^2 + 2xy + y^2 = 46^2.    (3)


Now subtract eq(2) from eq(3) (both sides).  The terms  x^2  and  y^2 will cancel each other, and you will get


2xy = 46^2 - 34^2  =  (46-34)*(46+34) = 12*80.


Hence,  xy =  = 6*80 = 480.


It is the area of the rectangle, which is under the question.


Answer.  The area of the rectangle is 480 square units.