Question 724247
{{{drawing(300,300,-35,35,-35,35,
circle(0,0,30),
rectangle(-9sqrt(10),-3sqrt(10),9sqrt(10),3sqrt(10)),
line(-9sqrt(10),-3sqrt(10),9sqrt(10),3sqrt(10)),
line(-9sqrt(10),3sqrt(10),9sqrt(10),-3sqrt(10)),
locate(-9sqrt(10),2,x),locate(-2,-3sqrt(10),3x)
)}}}
If you recall that a {{{90^o}}} angle inscribed in a circle intercepts an arc measuring {{{180^o}}}, you realize that the diagonals of the rectangle are diameters of the circle, so they measure {{{60}}}feet.
Each diagonal divides the rectangle into two congruent right triangles with sides measuring {{{x}}} feet and {{{3x}}}feet.
According to the Pythagorean theorem,
{{{x^2+(3x)^2=60^2}}} --> {{{x^2+9x^2=3600}}} --> {{{10x^2=3600}}} --> {{{x=sqrt(360)}}} --> {{{x=sqrt(36*100)}}} --> {{{x=sqrt(36)*sqrt(10)}}} --> {{{x=6sqrt(10)}}}
SO the sides of the rectangle measure
{{{highlight(6sqrt(10))}}}feet and {{{highlight(18sqrt(10))}}}feet.