A piece of wire 24 m long is cut into two pieces. One piece is bent into a square and the other is bent into a circle. (a) How much wire should be used for the square in order to maximize the total area? Incorrect: Your answer is incorrect. m (b) How much wire should be used for the square in order to minimize the total area?

Answer:A) 23 m; B) 12 mStep-by-step explanation:The larger the circle, the larger the total area will be.This means we want to use as much wire as possible for the circle.  If we use only 1 meter for the rectangle, this means each side would be 0.25 m; this makes the area of the rectangle 0.25(0.25) = 0.0625 m².This leaves us 24-1 = 23 m of wire for the circle.  This will be the distance around the circle, or the circumference.  The formula for circumference is C = 2πr; using 23 for C and 3.14 for π, we have23 = 2(3.14)r23 = 6.28rDivide both sides by 6.28:23/6.28 = 6.28r/6.283.66 = rThe formula for area is A = πr²; using 3.14 for π and 3.66 for r, we haveA = 3.14(3.66)² = 42.06 m².This makes the total area 42.06+0.0625 = 42.1225 m²B) The closer the amount of wire is to half of the total, the smaller the total area will be.If we cut the wire exactly in half, there will be 12 m for the rectangle; this means each side will be 12/4 = 3 m long.  This makes the area 3(3) = 9 m².This leaves us with 24-12 = 12 m for the circle.  This is the circumference; using 3.14 for π, we have12 = 2(3.14)r12 = 6.28rDivide both sides by 6.28:12/6.28 = 6.28r/6.281.91 = rThis makes the areaA = πr² = 3.14(1.91)² = 11.46This gives us a total area of 11.46+9 = 20.46 m²