Assign the following variables for the origina3l rectangle: let w = width let w + 8 = length and the area would be w(w + 8) = w² + 8w
No for the second rectangle: let (w + 4) = width and (w + 8 - 5) or (w + 3) = length Area = length x width or (w + 4)(w + 3) = w² + 3w + 4w + 12 using the foil method to multiply to binomials. Simplified Area = w² + 7w + 12
Now our problem says that the two area will be equal to each other, which sets up the following equation:
w² + 8w = w² + 7w + 12 subtract w² from both sides 8w = 7w + 12 subtract 7w from both sides w = 12 this is the width of our original rectangle recall w + 8 = length, so length of the original rectangle would be 20
