-------------------------------------- Define x: -------------------------------------- Let the width be x. Width = x Length = x + 2
-------------------------------------- Construct equation: -------------------------------------- x (x + 2) = 24 x² + 2x = 24 x² + 2x - 24 = 0 (x - 4) (x + 6) = 0 x = 4 or x = - 6 (rejected, length cannot be negative)
-------------------------------------- Find the length and Width -------------------------------------- Width = x = 4 Length = x + 2 = 4 + 2 = 6
---------------------------------------------------------------------------- Answer: The dimension is 6 feet by 4 feet. ----------------------------------------------------------------------------
Think of it this way: x multiplied by a number that is two more than x is y. So, look at the factors. 3 and 8 wouldn't work, because 8 is 5 longer than 3. 1 and 24 wouldn't work, because 24 is 23 more than 1. 12 and 2 is also not going to work; 12 is 10 more than 2. What you have left is 4 and 6. 6 is 2 more than 4, and they both multiply to get 24.
So, the correct answer is 6 feet long and 4 feet wide.
