Respuesta :
Answer:
The radius of the circle is 16.97 feet
Step-by-step explanation:
First, we will the determine the length of one the sides of the square lawn.
From the question,
The square lawn has an area of 1152 square feet,
Now, we can determine the length of a side of the square lawn from the formula,
[tex]A = l^{2}[/tex] ( Formula for Area of a square)
Where [tex]A[/tex] is the area of the square lawn
and [tex]l[/tex] is the length of a side of the square lawn
From the question, [tex]A[/tex] = 1152 square fee
Then,
[tex]1152 = l^{2}[/tex]
[tex]l^{2} = 1152\\l = \sqrt{1152}[/tex]
[tex]l = 24\sqrt{2}[/tex] feet or [tex]33.94[/tex] feet
This is the length of one of the sides of the square lawn.
From the description in the question, the sprinkler sprays water in a circular pattern that just covers the lawn,
If the circular pattern formed just covers the lawn,
then, the diameter of the circle equals the length of one of the sides of the square lawn, that is,
[tex]l = d[/tex]
Where [tex]d[/tex] is the diameter of the circle
Hence, [tex]d = 24\sqrt{2}[/tex] feet
This is the diameter of the circle.
Now, for the radius of the circle,
From the relation between radius and diameter,
[tex]Radius = \frac{Diameter}{2}[/tex]
Then,
[tex]Radius = \frac{24\sqrt{2} }{2}[/tex]
[tex]Radius = 12\sqrt{2}[/tex] feet or [tex]16.97[/tex] feet
Hence, the radius of the circle is 16.97 feet
