_____ If you're going to write an equation for width (w), you can write it as w(w+8) = 273 and simplify it to w² +8w -273 = 0 Solving this by factoring requires you find the factors of 273 that differ by 8, as above.
You can also solve by completing the square or using the quadratic formula. Those methods will tell you w is either of -21 or 13. Only the positive solution is applicable.
Another method I use mentally is to think of the equation in terms of the average of length and width (x). Then the area is (x-4)(x+4) = 273 x² -16 = 273 . . . . . this is a much easier quadratic to solve x² = 289 x = 17 . . . . . . . . you know this because you have the squares of small numbers memorized. Then the dimensions are 17-4 = 13, and 17+4 = 21.
