text: There is a rectangle, 6x8 inside of a larger rectangle.  The distance between the inner and outer is "x", and we're assuming it's uniform all the way around.\n\nSo the 6ft side of the rectangle has x on the left and x on the right, so the total side is 6 + 2x.  The 8ft side has x on top and x on bottom, or 8 + 2x total.\n\nArea is length * width, and you know total area, border and all, is 100.\n\n100 = (6+2x)(8+2x)\n\n100 = 48 + 28x + 4x^2 <--- you can divide through by 4 here\n\n25 = 12 + 7x + x^2; make the equation = 0 by subtracting 25 from both sides, and reorder a bit:\n\n0 = x^2 + 7x - 13\n\nNow use quadratic formula to solve for x; when ax^2 + bx + c = 0; x = [-b +/- sqrt(b^2 - 4ac)]/2a\n\nso for x^2 + 7x - 13 = 0 a is 1; b is 7; and c is -13\n\nx = [-7 +/- sqrt(7^2 - (4)(1)(-13)]/2*1 \n\n= [-7 +/- sqrt(49 + 52)]/2\n\n= [-7 +/- sqrt(101)]/2 <-- you would only consider the plus, since -7 minus sqrt101 would give you a negative number, thus your answer\n\nx = [-7 + sqrt(101)]/2 = approx. 1.52 ft