Question 1095481: A 1/4mile track for racing stock cars consists
of two semicircles connected by parallel straightaways.
In order to provide sufficient room for pit crews, emergency
vehicles, and spectator parking, the track must enclose an area of
100,000 square feet. Find the length of the straightaways and the diameter
of the semicircles to the nearest foot.
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! 1 mile is 5280 feet, so the 1/4 mile track has a perimeter measuring
 .
If  = radius of the semicircles, in feet, and
 = length of the straightaways, in feet,
the equations for the perimeter/length of the track,
and for the surface area enclosed by the track are
 <-->  and
All we have to do is solve the system of equations
 .
<--> 
and substituting into the other equation in the system,
 .
Applying the quadratic formula,
 
That gives 2 approximate values for R,
 -->  ,
which rounds to  , and
 -->  , which makes no sense.
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