Question 1170327
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Let x be the width, in inches;

then the length is (x+2) inches.


The area is  x*(x+2) square inches.


The perimeter is  2x + 2*(x+2) = 4x + 4 inches.


The equation is  

    x*(x+2) - (4x+4) = 31,   or


    x^2 +2x - 4x + 2 - 4 = 31

    x^2 - 2x - 35 = 0

    (x-7)*(x+5) = 0.


Of the two roots  x= 7, x= -5, only value of 7 is positive and is the solution to the problem.


The dimensions of the rectangle are  7 and 9 inches.      <U>ANSWER</U>


<U>CHECK</U>.  The area is 7*9 = 63 sq.inches.  The perimeter is  2*(7+9) = 32 inches.  The difference is  63 - 32 = 31.   ! Correct !
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Solved.