A = Lw (area of rectangle is length times width) A = 15 (Area is 15) L = 2x + 5 (length is 2 times a number plus another 5) w = x - 4 (width is 4 less than that number
Plug in the values: 15 = (2x + 5)(x - 4) FOIL 15 = 2x2 - 8x + 5x - 20 simplify: 15 = 2x2 - 3x - 20 Subtract 15 0 = 2x2 - 3x - 35 Factor out the quadratic. We know that one number has to be 7 and the other 5 so that they multiply together to make 35, and that one of them has to be negative so that it's actually -35. That means we have m * n = -35 We also need it set up so that so that 2m + n = -3: 2 * -5 + 7 = -3 0 = (2x + 7)(x - 5) So: 0 = 2x + 7, or 0 = x - 5 x = -7/2 or 5 We cannot have a negative length, so x = 5
