Your grandmother has asked you to help her build a rectangular garden for her roses in her back yard. She has 120 feet of fencing and plans to have one side of the garden against the back of her house so it doesn’t need fencing. What are the dimensions (length and width) of the garden that would give her the maximum possible area for growing her beloved roses?

Question

Your grandmother has asked you to help her build a rectangular garden for her roses in her back yard.  She has 120 feet of fencing and plans to have one side of the garden against the back of her house so it doesn’t need fencing.  What are the dimensions (length and width) of the garden that would give her the maximum possible area for growing her beloved roses?

R_scott · Answer

L + 2 W = 120 ... L = 120 - 2W area = L * W = (120 - 2W) * W = 120 W - 2 W^2 the maximum is on the axis of symmetry ... -b / 2a Wmax = -120 / (2 * -2) substitute back to find Lmax