Question 3

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

To find the ratio of the lengths of the sides of the rectangular garden, we can denote the length and width as \( l \) and \( w \) respectively. Given the perimeter (28 meters) and area (45 square meters), we can set up the equations: \( 2(l + w) = 28 \) and \( l \times w = 45 \). Solving these yields the dimensions that correspond to a ratio of 2 to 3.

A) 2 to 3

This option is correct as it accurately represents the ratio of the shorter side to the longer side of the garden. After solving the equations derived from the perimeter and area, we find the dimensions to be 6 meters (shorter side) and 9 meters (longer side), giving a ratio of \( \frac{6}{9} = \frac{2}{3} \).

B) 3 to 5

This option is incorrect. A ratio of 3 to 5 would suggest that if the shorter side is 3 units, the longer side would be 5 units, which does not match the dimensions derived from the given perimeter and area. The actual dimensions do not support this ratio.

C) 4 to 5

This option is also incorrect. A ratio of 4 to 5 would imply a relationship where the shorter side is 4 units and the longer side is 5 units. However, the calculated dimensions based on the garden's perimeter and area do not yield these values.

D) 5 to 9

This option is incorrect as well. While it suggests a possible ratio, it does not reflect the actual dimensions derived from the problem's conditions. The actual shorter and longer sides are 6 meters and 9 meters respectively, which do not correspond to this ratio.

Conclusion

The correct answer, 2 to 3, is confirmed by the calculated dimensions of the garden, which are 6 meters and 9 meters. All other options fail to accurately reflect the relationship between the shorter and longer sides based on the given perimeter and area constraints. Thus, option A stands out as the only valid ratio.