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A square lawn has aroa 3200 ft^2. A sprinkler placed at the center of the lawn sprays water in a circular pattern as shown in the figure. What is the radius of the circle?The radius of the circle is ___ ft.(Simplify your answer. Use a comma to separate answers as needed.)

A square lawn has aroa 3200 ft^2. A sprinkler placed at the center of the lawn sprays-example-1
User Jbbae
by
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1 Answer

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Answer: The radius of the circle is 40 ft.

Step-by-step explanation

• The square lawn area is 3200 ft².

The formula for the area of a square (A) is:


A=s^2

where s represents the side.

If we replace the area, we can find the side:


s^2=3200


√(s^2)=√(3200)
s=40√(2)

If the sprinkler is placed at the center of the lawn spraying water in a circular pattern that covers the lawn, the diameter ( d ) of the circle is equal to the diagonal of the square:


d=√(s^2+s^2)

Replacing the values:


d=√(3200+3200)

Simpifying:


d=√(6400)


d=80ft

However, as the radius ( r ) is half the diameter then:


r=(d)/(2)
r=(80)/(2)=40

The radius is 40ft.

User Sandeep Sherpur
by
8.2k points
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