Question 5

The ratio of the length of the shorter side to the length of the longer side is 2 to 3.

To determine the ratio of the shorter side to the longer side of the rectangular garden, we find that the dimensions of the garden are 6 meters and 3 meters, yielding a ratio of 2 to 3.

A) 2 to 3

This option is correct because the dimensions of the garden can be derived from the equations of perimeter and area. The perimeter is given by 2(length + width) = 28 meters, which simplifies to length + width = 14 meters. The area is given by length × width = 45 square meters. Solving these equations leads to the dimensions being 6 meters and 3 meters, resulting in the ratio of the shorter side to the longer side as 3:6 or simplified to 2:3.

B) 3 to 5

This option is incorrect because it does not reflect the calculated dimensions of the garden. The ratio of 3 to 5 implies that if the shorter side were 3 units, the longer side would be 5 units, which does not match the actual dimensions derived from the perimeter and area provided.

C) 4 to 5

This option is also incorrect. A ratio of 4 to 5 suggests that if the shorter side were 4 units, the longer side would be 5 units. However, the actual dimensions of the garden do not correspond to this ratio, as calculated from the given perimeter and area.

D) 5 to 9

This option is incorrect as well. The ratio of 5 to 9 would indicate that if the shorter side were 5 units, the longer side would be 9 units. This is inconsistent with the established dimensions of the garden, which are 3 meters and 6 meters, leading to a ratio of 2 to 3.

Conclusion

The correct answer is 2 to 3 because it accurately represents the ratio derived from the garden's dimensions of 3 meters and 6 meters. All other options fail to match the calculated dimensions based on the garden's perimeter and area, confirming that they are not viable answers to the question.