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a running track has a straight legs of length 100 yards that are 60 yards apart.

Mathematics
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a running track has a straight legs of length 100 yards that are 60 yards apart. what is the length of the (inner lane of the track), including the circular legs, and what is the area of the infield of the track?

Apr 28th, 2015

The length/perimeter is the straight lengths plus the circular lengths which could be expressed as the circumference of an entire circle with diameter of 60y since that would be the length of the circular parts combined together. 

Circumference = pi(diameter) = 60pi(y)

Perimeter would be 60pi(y) + 100y + 100y = 200y + 188y = 388y

The area can be divided into 2 sections added together: the circular part which again is the area of a circle with a diameter of 60y and the rectangular section which is 100y X 60y

The area = pi(30y)^2 + 100y X 60y

A = pi(900y)^2 + 6,000y^2

A = 2,827y^2 + 6,000y^2 

A = 8,827y^2

Apr 28th, 2015

thanks

May 1st, 2015

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