Step-by-step explanation:
you know what the perimeter is ?
it is the whole way around an object.
so, look at the picture.
let's say, we start at one of the corners of the implicit rectangle.
then we go along one long straight line, then follow a half-circle, then go along another long straight line, and then follow another half-circle.
we do know already the lengths of the straight long lines : 120m each.
what do we know about the half-circles ?
at a first glimpse seemingly nothing, but that really only seems so.
what is the circumference (= the perimeter) of a circle ?
C = 2×pi×r
r = radius. it is the only thing we need, as the other 2 factors we know.
so, look at the picture again.
what is the radius of the half-circles on both ends (both half-circles clearly have the same radius, because it is a rectangle in the middle) ?
it is half of the short side of this inner rectangle.
aha, so, to get the radius for the half-circle calculations, we need first to find the length of the shirt side of the rectangle.
now we know why we were given also the area of the rectangle.
the area of a rectangle Ar is
Ar = length×width = long side × short side
7200 = 120 × short side
short side = 7200/120 = 720/12 = 60 m
therefore, as said before, the radius of the half-circles is half of this short side (the whole long side is the diameter of these circles/half-circles).
radius = 60/2 = 30 m
so, the circumference of the full circles is
2×pi×30 = 2×3.14×30 = 188.4 m
we can keep the full circle circumference, because when "adding" both half-circles at both ends of the track we actually deal with one full circle anyway.
so, the perimeter of the track is the sum of 2 times the long straight line plus the circumference of the circle :
P = 2×120 + 188.4 = 240 + 188.4 = 428.4 m
