SOLUTION: please help me with world problems i have no clue where to even begin, please help!! An adjustable water sprinkler that sprays water in a circular pattern is placed at the cent

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Question 187801: please help me with world problems i have no clue where to even begin, please help!!
An adjustable water sprinkler that sprays water in a circular pattern is placed at the center of a square field whose area is 1250 square feet. What is the shortest radius setting that can be used if all of the grass is to be watered?
thank you!
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
Let s = side length of the square, d = diagonal of the square

It turns out that the radius must be equal to half the diagonal "d" in order to water all of the grass since the distance to the corner (from the center) is the largest.

So let's draw the picture:

From the drawing, we can see that the radius of the circle "r" is half the diagonal which means

Since the area of the square is 1250 square feet. This means that

Start with the area of a square formula

Plug in

Rearrange the equation.

Now, by the Pythagorean Theorem , we can see that the sides "s" form the legs of a triangle with a hypotenuse "d"

So , , and

Plug this in to get:

Combine like terms.

Plug in

Multiply

Rearrange the equation.

Take the square root of both sides (note: we're only considering the positive square root).

Take the square root of 2500 to get 50

Go to the formula dealing with the radius

Plug in

Multiply

Reduce

So the radius must be 25 feet in order for the entire lawn to be watered.