Question 187801
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:



<img src="http://i150.photobucket.com/albums/s91/jim_thompson5910/Algebra%20dot%20com/circle.png">



From the drawing, we can see that the radius of the circle "r" is half the diagonal which means {{{r=(1/2)*d}}}



Since the area of the square is 1250 square feet. This means that {{{A=1250}}}



{{{A=s^2}}} Start with the area of a square formula



{{{1250=s^2}}} Plug in {{{A=1250}}}



{{{s^2=1250}}} Rearrange the equation.




Now, by the Pythagorean Theorem {{{a^2+b^2=c^2}}}, we can see that the sides "s" form the legs of a triangle with a hypotenuse "d"



So {{{a=s}}}, {{{b=s}}}, and {{{c=d}}}



Plug this in to get: {{{s^2+s^2=d^2}}}



{{{2s^2=d^2}}} Combine like terms.



{{{2(1250)=d^2}}} Plug in {{{s^2=1250}}}



{{{2500=d^2}}} Multiply



{{{d^2=2500}}} Rearrange the equation.



{{{d=sqrt(2500)}}} Take the square root of both sides (note: we're only considering the positive square root).



{{{d=50}}} Take the square root of 2500 to get 50



{{{r=(1/2)*d}}} Go to the formula dealing with the radius



{{{r=(1/2)*(50)}}} Plug in {{{d=50}}}



{{{r=50/2}}} Multiply



{{{r=25}}} Reduce



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