I will need help with the two problems please and please make it legible

X Use the method of Lagrange multipliers to find the dimensions of the rectangle of greatest area that can be inscribed in the ellipse 9 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 = Width = (Type exact answers, using radicals as needed.)Write an iterated integral fordA over the region R bounded by y = Vx, y =0, and x = 243 using R a) vertical cross-sections, b) horizontal cross-sections. . . . . . a) Choose the correct iterated integral using vertical cross-sections below. O A. OB. 243 VX O c. VX 243 OD. J J ax dy VX 243 243 VX o J Jaxdy o b) Choose the correct iterated integral using horizontal cross-sections below. O A. O B. 243 3 O C. 3 243 O D. 243 3 3 243 y5 0 S Sax dy I S ax dy