Question

Miranda has 55 feet of fencing. She wants to use all the fencing to create a rectangular garden. The equation 21 + 2w = 55, where l is the length of the garden and w is the width, models the scenario. This equation can be used to find one dimension of the garden if the other dimension is known. Think about constraints. Each side must be greater than 0. Each side must be less than or equal to 27.5. Each side must be greater than a (__) inches.

Options:
a) 10
b) 15
c) 20
d) 25

Answer 1

The most reasonable constraint for the minimum length each side of the garden must be, considering the fencing length and practical construction standards, is 10 inches.

Step-by-step explanation:

The question revolves around finding constraints for the dimensions of a rectangular garden given the total length of fencing available. Since the fencing is 55 feet in total and must form a rectangle, this implies the constraint for the length and width that both must be greater than 0 feet but no greater than 27.5 feet each.

However, the question seems to focus on a detail regarding the minimum size in inches for each side, which suggests a discussion about practical limitations such as the spacing of fence posts or construction standards that require each side to be greater than a certain length in inches.

Given the fencing length constraint, the smallest value in the options provided which aptly conveys a reasonable practical limit to the construction would be option a) 10 inches for each side's minimum length. This allows for a sufficiently small granularity in fence post spacing while still providing a sizable enough increment to ensure stability and structure of the garden fence.