question: Simon has a certain length of fencing to enclose a rectangular area. The quadratic function A with a vertec of (10, 100) models the rectangle's area (in square meters) as a function of its width (in meters). It intersects with x-axis at (0,0) and (20,0). Which of these statements are true?
  Choices:
  A:Greater width always relates to smaller area.
  B:Greater width relates to smaller area as long as the width is less than $10 \mathrm{~m}$.
  C:When there is no width, the area is $20 \mathrm{~m}^2$.
  D:When there is no width, the area is $0 \mathrm{~m}^2$.
query_wo: Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.
  Question: Simon has a certain length of fencing to enclose a rectangular area. The quadratic function A with a vertec of (10, 100) models the rectangle's area (in square meters) as a function of its width (in meters). It intersects with x-axis at (0,0) and (20,0). Which of these statements are true?
  Choices:
  A:Greater width always relates to smaller area.
  B:Greater width relates to smaller area as long as the width is less than $10 \mathrm{~m}$.
  C:When there is no width, the area is $20 \mathrm{~m}^2$.
  D:When there is no width, the area is $0 \mathrm{~m}^2$.
query_cot: Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
  Question: Simon has a certain length of fencing to enclose a rectangular area. The quadratic function A with a vertec of (10, 100) models the rectangle's area (in square meters) as a function of its width (in meters). It intersects with x-axis at (0,0) and (20,0). Which of these statements are true?
  Choices:
  A:Greater width always relates to smaller area.
  B:Greater width relates to smaller area as long as the width is less than $10 \mathrm{~m}$.
  C:When there is no width, the area is $20 \mathrm{~m}^2$.
  D:When there is no width, the area is $0 \mathrm{~m}^2$.
question_for_eval: Simon has a certain length of fencing to enclose a rectangular area. The quadratic function A with a vertec of (10, 100) models the rectangle's area (in square meters) as a function of its width (in meters). It intersects with x-axis at (0,0) and (20,0). Which of these statements are true?
  Choices:
  A:Greater width always relates to smaller area.
  B:Greater width relates to smaller area as long as the width is less than $10 \mathrm{~m}$.
  C:When there is no width, the area is $20 \mathrm{~m}^2$.
  D:When there is no width, the area is $0 \mathrm{~m}^2$.