(2) Answers
Each wire is now 4 meters long.
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.
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