The sides of the rectangle of greatest area that can be inscribed in the ellipse $x^2+4 y^2=64$ are :

• A

  $(6 \sqrt{2}, 4 \sqrt{2})$
• Correct answer
  B

  $(8 \sqrt{2}, 4 \sqrt{2})$
• C

  $(8 \sqrt{2}, 8 \sqrt{2})$
• D

  $(16 \sqrt{2}, 4 \sqrt{2})$

Hence, the correct answer is option: 'B'.