Question 1170327
let x be the width
let x+2 be the length
A=area
P=perimeter
A=lw
 =x(x+2)
A=x²+2x

P=2x+2(x+2)
 =2x+2x+4
P=4x+4
The equation is:
  area-perimeter=31
  (x²+2x)-(4x+4)=31
  x²+2x-4x-4=31
  x²-2x-4-31=0
  x²-2x-35=0
by completing the square:
   x²-2x+1=35+1
   (x-1)²=36
   √(x-1)²=±√36
    x-1=±6
Take the positive value of the roots/factors
    x=1+6
    x=7 - the width
Substitute the value of x to the length representation:
    x+2= 7+2= 9-the length
Perimeter: Substitute the positive value of the root(width) to:
   P=4x+4
    =4(7)+4
   P=32"