Answer:
John should purchase approximately 9.6 gallons of paint. Since you typically can't purchase a fraction of a gallon, it would be advisable for John to round up to the nearest whole number. Thus, John should purchase at least 10 gallons of paint.
Explanation:
Given information:
Length of the yard = 30 feet
Width of the yard = 20 feet
Height of the fence = 3 feet
Length of the house side (not to be painted) = 30 feet
The area of each side of the yard that needs to be painted is the height of the fence multiplied by the length of the yard. Since there are two sides to be painted, we have:
Area of each side = Height of fence * Length of yard
Area of each side = 3 feet * 30 feet
Area of each side = 90 square feet
Now, we need to calculate the perimeter of the yard:
Perimeter of the yard = 2 * (Length + Width)
Perimeter of the yard = 2 * (30 feet + 20 feet)
Perimeter of the yard = 2 * 50 feet
Perimeter of the yard = 100 feet
Since the entire perimeter of the yard needs to be painted, the area is equal to the height of the fence multiplied by the perimeter:
Area of perimeter = Height of fence * Perimeter of the yard
Area of perimeter = 3 feet * 100 feet
Area of perimeter = 300 square feet
To find the total area that needs to be painted, we add the areas of the two sides and the perimeter:
Total area = 2 * Area of each side + Area of perimeter
Total area = 2 * 90 square feet + 300 square feet
Total area = 180 square feet + 300 square feet
Total area = 480 square feet
Given that one gallon of paint covers 50 square feet, we can now calculate the number of gallons John should purchase:
Number of gallons = Total area / Coverage per gallon
Number of gallons = 480 square feet / 50 square feet
Number of gallons = 9.6