Question

A square lawn has area 512 ft squared .ft. a sprinkler placed at the center of the lawn sprays water in a circular pattern that just covers the lawn. what is the radius of the​ circle?

Answer 1

Radius of circle = 16 ft

Explanation:

Refer figure for the arrangement.

Area of square = 512 ft²

Side of square
`=√(512)=22.63ft`

From figure see that

Diagonal of square = Diameter of circle

`\texttt{Diameter of circle}=√(22.63^2+22.63^2)=32ft`

Radius of circle
`=(32)/(2)=16ft`

Answer 2

The side length of the square is √512 ft = 16√2 ft. Then the radius of the circle is that distance divided by √2, so is 16 feet.