Question

You are fencing in a rectangular area of a garden you have only 150 feet of fence do you want the length of the garden to be at least 40 feet you want the width of the garden to be at least 5 feet what is a graph showing the possible dimensions your garden could have? What vegetables will you use? What will they represent? How many inequalities do you need to write?

Answer 1

Length ≥ 40

Width ≥ 5

Perimeter = 2 × (Length + Width)

2 × (Length + Width) ≤ 150

Explanation:

To create a graph showing the possible dimensions of the garden, we need to plot the length and width of the rectangular area on the x and y axes, respectively. Since we want the length to be at least 40 feet and the width to be at least 5 feet, we can represent these constraints by the following inequalities:

Length ≥ 40

Width ≥ 5

We also know that the total length of fencing available is 150 feet, which means that the perimeter of the rectangular area must be less than or equal to 150 feet. The perimeter of a rectangle is given by:

Perimeter = 2 × (Length + Width)

So, we can write the inequality representing the perimeter as:

2 × (Length + Width) ≤ 150

To graph the possible dimensions of the garden, we can plot the points that satisfy all three inequalities on the x-y plane.

Regarding the vegetables, it is not clear what vegetables the user would like to plant in the garden. As such, we cannot provide a specific answer to this question.

In summary, we need to write three inequalities to represent the constraints in the problem, and we can graph the solution space using these inequalities.