A rotating sprinkler sprays water in a circle in a yard and covers an area of 81π square feet. What is the radius of the circle that is watered?

1. Width = x + 2

2. Length = 12; width = 9

3. x² + 7x + 10

4. 108

Step-by-step explanation:

perimeter = 4x + 14

length = x + 5

1. Perimeter of a rectangle = 2(length + width)

4x + 14 = 2{(x + 5) + width}

4x + 14 = 2x + 10 + 2width

4x + 14 - 2x - 10 = 2width

2x + 4 = 2width

Width = (2x + 4)/2

Width = x + 2

2. Perimeter of a rectangle = 2(length + width)

42 = 2{(x + 5) + (x + 2)}

42 = 2x + 10 + 2x + 4

42 = 4x + 14

42 - 14 = 4x

28 = 4x

x = 28/4

x = 7

length = x + 5

= 7 + 5

= 12

Width = x + 2

= 7 + 2

= 9

3. Area of the rectangle = length × width

= (x + 5)(x + 2)

= x² + 2x + 5x + 10

= x² + 7x + 10

4. Area of the rectangle = x² + 7x + 10

When x = 7

x² + 7x + 10

= 7² + 7(7) + 10

= 49 + 49 + 10

= 108