Question

You are building a rectangular garden against the back of your house using 80 feet of fencing. The area of the garden needs to be greater than 400 square feet but less than 600 square feet.

Which interval(s) represent possible lengths, in feet, for the horizontal edges of the garden?
a. (0,10)∪(30,40)
b. (20− 2,20+10)
c. (0,20−10 )∪(20+ 2)
d. (20,10)∪(30,20+10)
Please choose the correct option representing the possible lengths for the horizontal edges of the garden based on the given conditions.

Answer 1

To solve this problem, set up an inequality using the perimeter and area of the garden. Graph the equations and find the intersection of the solutions. The correct intervals for the horizontal edges of the garden are c. (0,20-10) ∪ (20+2,30).

Step-by-step explanation:

To solve this problem, we can set up an inequality using the perimeter of the garden and the given conditions. Let's assume the lengths of the horizontal edges of the garden are x and y.

1. The perimeter of the garden is the sum of the lengths of all four sides, which is given as 80 feet.
2. The area of the garden is the product of the lengths of the horizontal edges, which needs to be greater than 400 square feet but less than 600 square feet.

Using these conditions, we can set up the following inequality:

2x + 2y = 80

x * y > 400

x * y < 600

To solve this system of inequalities, we can graph the equations and find the intersection of the solutions.

After analyzing the given options, the correct interval(s) that represent possible lengths for the horizontal edges of the garden are (0,20-10) ∪ (20+2,30).