A wire 8 meters long is cut into two pieces.

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.

Each wire is now 4 meters long.