Question 1172178
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Let the uniform width of the frame be " x " inches.


Then the outer dimensions of the frame are  8+2x and 12+2x.


From the condition, you have this equation

    (8+2x)*(12+2x) - 8*12 = 8*12.


Reduce it to the standard form quadratic equation

    96 + 16x + 24x + 4x^2 - 96 = 96

    4x^2 + 40x - 96 = 0

     x^2 + 10x - 24 = 0

     (x+12)*(x-2) = 0.


This equation has two root, -12 and 2.

Of them , only positive value makes sense.


<U>ANSWER</U>.  The uniform width of the frame is  2 inches.
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Solved.