John is planting a rectangular garden that is 2 feet wide. He hasn’t decided how long to make it, but he’s considering 4 feet, 5 feet, and 6 feet. He wants to put a short fence around the garden to keep the rabbits out. What are John’s options if he has a budget of $40 and the cost of the fencing is approximately $1.75 per linear foot?
The "perimeter" is the distance around the rectangle; perimeter = the sum of each side
If John makes the garden 2 ft by 4 ft, the perimeter is 2 ft + 4 ft + 2 ft + 4 ft or 12 ft
You can simplify the expression to perimeter = 2(2 ft + 4 ft) = 12 ft
If John makes the garden 2 ft by 5 ft, the perimeter is 2(2 ft + 5 ft) = 14 ft
If John makes the garden 2 ft by 6 ft, the perimeter is 2(2 ft + 6 ft) = 16 ft
Next figure out how much fencing he can afford: $40 / ($1.75/ft) = 22.9 ft
Since the largest size garden he is considering requires 16 ft of fencing and he has enough to pay for almost 23 ft of fencing, he can easily make the largest size he is considering, 2 ft by 6 ft, or any size smaller.
