Question

A gardener is planning to fill her garden with mulch. she plots it on a grid to plan how much she will need. the garden is in the shape of a rectangle with vertices at ( 2 , 5 ) , ( 8 , 5 ) , ( 8 , 3 ) , and ( 2 , 3 ) . one bag of mulch covers 6 ft 2 and costs $5.25. how much will it cost her to cover her garden? show all of your work.

Answer 1

The gardener will need 2 bags of mulch to cover the 12 square feet of the garden, with the total cost amounting to $10.50.

Step-by-step explanation:

To calculate the cost of covering the garden with mulch, we first need to determine the area of the rectangular garden. The garden has vertices at (2, 5), (8, 5), (8, 3), and (2, 3). The length of the garden can be found by subtracting the x-coordinates of the vertices along the same horizontal line, which is 8 - 2 = 6 feet. Similarly, the width can be found by subtracting the y-coordinates of the vertices along the same vertical line, which is 5 - 3 = 2 feet. Thus, the area of the garden is 6 feet × 2 feet = 12 square feet.

Since one bag of mulch covers 6 square feet and costs $5.25, the gardener will need 2 bags to cover the entire garden (12 square feet / 6 square feet per bag). The total cost will be 2 bags × $5.25 per bag = $10.50.