a wire of 50cm, is cut into 2 pieces. One piece is folded into a square. The other piece is bent into a circle. What cut length would make them equal size?

Answer 1

Two different relationships here.

1: area of the square = area of the circle

2. Circumference of the square + circumference of the circle = 50 (cm)

1. X^2 = πr^2

2. 4x + 2πr = 50

From 1, x = √π r

Plug it into 2, simplify to get r = 50/4* (√π) + 2π

R ~ 3.7389 cm

Circum of circle = 2πr =~ 23.5 cm

Circum of square = 26.5 cm