we know that
area of rectangle=length*width
let
x-----> the length side
y-----> the width side
y=13 units
A=2x²-5x
A=x*y------> 2x²-5x=x*13------> 2x²-18x=0-----> x²-9x=0
x*(x-9)=0
the solutions are
x=0
x=9
hence
the dimensions of the rectangle are
length is 9 units
width is 13 units
the area of rectangle is -----> 9*13-----> 117 units²
the answer is
117 units²