Question

question 2-16
a garden is composed of a rectangle and semicircles on each side. the house is on one side of the garden as shown.
the homeowner wants to cover the garden in mulch. one bag of mulch will cover 12 square feet and costs $4.
answer the questions below.
the garden has an area over 150 square feet. true false
the homeowner will need to purchase blank whole bags of mulch to cover the garden.
the homeowner can cover the garden in mulch for less than $50. blank

Explanation:

Step1: Calculate area of rectangle

The rectangle has length 15 ft and width 7 ft. Area of rectangle is \( \text{length} \times \text{width} = 15 \times 7 = 105 \) square feet.

Step2: Calculate area of circle (two semicircles)

Two semicircles make a full circle. Radius \( r = \frac{7}{2} = 3.5 \) ft. Area of circle is \( \pi r^2 = \pi \times (3.5)^2 \approx 38.48 \) square feet.

Step3: Total area of garden

Total area = area of rectangle + area of circle \( \approx 105 + 38.48 = 143.48 \) square feet. Since \( 143.48 < 150 \), the statement "The garden has an area over 150 square feet" is False.

Step4: Number of mulch bags

Total area \( \approx 143.48 \) sq ft. Each bag covers 12 sq ft. Number of bags \( = \lceil \frac{143.48}{12}
ceil = \lceil 11.956
ceil = 12 \) bags.

Step5: Cost of mulch

Cost per bag is $4. Cost for 12 bags LXI0 dollars, which is less than $50. So "The homeowner can cover the garden in mulch for less than $50" is True.

Answer:

s:

1. The garden has an area over 150 square feet: False
2. The homeowner will need to purchase 12 whole bags of mulch to cover the garden.
3. The homeowner can cover the garden in mulch for less than $50: True