Question
A wire 360 cm long is cut into two pieces. One piece is formed into a square and the other into a circle. If the two figures have the same area, what are the lengths of the two pieces of wire (to the nearest tenth of an centimeter)? Take the length of the circle to be x cm.
Answers
pi r^2 = s^2
4 s + 2 pi r = 3600
it seems they want you to use x for 2 pi r so
r = x/(2pi)
pi r^2 = x^2/(4 pi) = s^2
so
4 s + x = 360
2x/( sqrt pi) + x = 360
2.13 x = 360
x = 169.1 cm
360 - x = 4s = 190.9 cm
s = 47.7
-------------------------
check
r = x/(2 pi) = 26.9
pi r^2 = 2276
s^2 = 2277 close enough
4 s + 2 pi r = 3600
it seems they want you to use x for 2 pi r so
r = x/(2pi)
pi r^2 = x^2/(4 pi) = s^2
so
4 s + x = 360
2x/( sqrt pi) + x = 360
2.13 x = 360
x = 169.1 cm
360 - x = 4s = 190.9 cm
s = 47.7
-------------------------
check
r = x/(2 pi) = 26.9
pi r^2 = 2276
s^2 = 2277 close enough