A farmer is planning to build a rectangular vegetable garden. The length of the garden is always 3 meters more than twice the width. The farmer has enough fencing material to enclose a total perimeter of 60 meters.

Question

In the context of this problem what are the constraints for the viable solutions?

(1 point)
Responses

No constraints
No constraints

All positive integers
All positive integers

All positive integers greater than zero
All positive integers greater than zero

All real numbers

Answer 1

The constraints for the viable solutions in this context involve both the physical measurements of the garden and the restrictions imposed by the given conditions.

1. The dimensions of the garden (length and width) must be positive, as negative or zero dimensions would not make sense in the context of a physical garden.
2. The total perimeter of the garden must equal 60 meters.

Given that the length \( L \) is expressed in terms of the width \( W \) as \( L = 2W + 3 \), we can use the perimeter formula for a rectangle:

\[ P = 2L + 2W = 60. \]

Substituting for \( L \):

\[ 2(2W + 3) + 2W = 60. \]

Now solving this will further confirm that \( W \) must be greater than zero.

Thus, the correct constraint for the viable solutions is:

All positive integers greater than zero.