length $90$ feet and width $70$ feet
Work Step by Step
Step 1. Assume the dimension of the length is $x$ feet and the other side is $y$ feet; we have the perimeter as $2x+2y=320$ or $x+y=160$ and $y=160-x$ Step 2. The total cost is given by $16x+2(5)y=2140$ or $8x+5y=1070$ Step 3. Use substitution; we have $8x+5(160-x)=1070$ or $3x=270$ and $x=90$ feet. Thus, $y=70$ feet.