Find the dimensions of the rectangle

(a) The sum of length and width is half the perimeter, so the breadth in terms of length (x) in cm will be
.. breadth = 34 -x

(b) Then the expression for the area (in cm^2) is
.. area = length*breadth
.. 253 = (x)(34 -x)
.. x^2 -34x +253 = 0 . . . . . subtract the right side, eliminate parentheses
.. (x -11)(x -23) = 0 . . . . . . . factor
.. x = 11 or 23

The dimensions of the rectangle are 11 cm by 23 cm.

Cis your correct answer