Question 16

The ratio of the shorter side to 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 that meet the given perimeter and area conditions yield a ratio of 2 to 3.

A) 2 to 3

This option is correct as it represents the ratio of the shorter side to the longer side derived from the dimensions of the garden. By solving the equations formed by the perimeter (2(l + w) = 28) and area (l * w = 45), we find the length and width to be 6 m and 4 m respectively, resulting in a ratio of 4:6, which simplifies to 2:3.

B) 3 to 5

This option is incorrect because the ratio of 3 to 5 does not correspond to the dimensions obtained from the perimeter and area calculations. The calculated side lengths do not support this ratio, as the actual dimensions are 4 m and 6 m.

C) 4 to 5

This option is incorrect as well. The ratio of 4 to 5 does not accurately reflect the relationship between the shorter and longer sides of the garden. The dimensions calculated from the perimeter and area do not yield a shorter side of 4 m and a longer side of 5 m.

D) 5 to 9

This option is incorrect since the ratio of 5 to 9 does not represent the dimensions of the garden based on the provided perimeter and area. The actual dimensions are 4 m and 6 m, and this ratio does not apply to those lengths.

Conclusion

The correct answer is 2 to 3, as it accurately describes the ratio of the shorter side to the longer side derived from the garden's dimensions. All other options fail to reflect the actual dimensions calculated from the perimeter and area, confirming that 2 to 3 is the only valid ratio.