I got this question wrong on a test, I know I set up my expression incorrectly but I don't know how/where. Can I please ask that when you reply, to include as much detail as possible so I understand how I went wrong?

Use the method of Lagrange multipliers to find the dimensions of the rectangle of greatest area that can be inscribed in the ellipse x^2/25+y^2/4=1 with sides parallel to the coordinate axes.

X Use the method of Lagrange multipliers to find the dimensions of the rectangle of greatest area that can be inscribed in the ellipse 25 4 =1 with sides parallel to the coordinate axes. Let length be the dimension parallel to the x-axis and let width be the dimension parallel to the y-axis. Length = 51/2 Width = 21/2 (Type exact answers, using radicals as needed.)