Constructing a stadium A track and field playing area is in the shape of a rectangle with semi circles at each end. The inside perimeter of the track is to be 1500 meters what should the dimensions of the rectangle be so that the area of the rectangle is a maximum? Constructing a stadium A track and field playing area is in the shape of a rectangle with semi circles at each end. The inside perimeter of the track is to be 1500 meters what should the dimensions of the rectangle be so that the area of the rectangle is a maximum? @Mathematics

jimmy did u got this one??

area = xy + pi(x/2)^2 where x = width and y = length of rectangle perimeter = 2y + 2pi(x/2) = 1500 y = [ 1500 - 2pi(x/2)] / 2 im not sure sheg - i've assumed he wants maxm area of the whole area - but he wants maxm area of rectangle!! so im confused

i feel as mentioned inside perimeter so perimeter os semi-circles which are inside then peri-meter of the circle is 2pie*r right

are you sure about the question uhveis?

right

answer should be in the dimension of a square or so,,,,,,,,,its my intution i m not sure logically

yes - if its maxm area of the rectangle then thats a square

there for on solving we will get radius equal to 238.64 m thus, width of rectangle is 2*238.64 m = 477.28 m

yes

and width will also be same. \hence dimension of the rectangle will be of a square

yea

is my intution correct @ jimmy

hey uhvei is it a square??????

i think so - if he wants maxm area of rectangle and not the whole field then thats correct.

the question is a bit confusing - i 'm surprised you dont want the maxm area of the whole field. are you studying calculus uhvei?

yeah its a parabola and i'm a girl we want the max of the rectangle i know thats what confused me too

srry im so late iw as trying to figure it out I think i'm on a path of getting it but i'm not sure

size of the rectangle 375 m x 238.73 m

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