Question

A wire 8 meters long is cut into two pieces.

Answer 1

Each wire is now 4 meters long.

Answer 2

  x = radius of circle 
y = side of triangle 
Total length = 3y + 2πx = 8 
total area = y²√3/4 + πx² 

3y + 2πx = 8 
y = (8–2πx)/3 
A = y²√3/4 + πx² 
A = [(8–2πx)/3]²√3/4 + πx² 

A = √3/36(8–2πx)² + πx² 
A = √3/9(4–πx)² + πx² 
A = √3/9(16–8πx+π²x²) + πx² 
A = (16/9)√3 – (8/9)√3πx + (√3/9)π²x² + πx² 
A = (√3/9+1)π²x² – (8/9)√3πx + (16/9)√3 

differentiate, set equal to zero and solve for x 

A' = 2(√3/9+1)π²x – (8/9)√3π = 0 
2(√3/9+1)πx = (8/9)√3 

x = (8/9)√3 / 2(√3/9+1)π = 1.5396 / 7.492 = 0.205 
check the arithmetic.