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# a wire of length 20 m is to be cut into two pieces.one of the pieces will be bent into shape of a square and the other into shape of an equilateral triangle.where the wire should be cut so that the sum of the areas of the square and the triangle is minimum?

Arun Kumar IIT Delhi
6 years ago
Hi

$\\a+b=20=>{da \over db}=-1 \\({a \over 4})^2+{b^2\sqrt3 \over 4 *3^2}=A \\=>2*{a \over 16}*{da \over db}+{b\sqrt3 \over 2 *3^2}=0 \\=>-{a \over 8}+{ b \sqrt3 \over 2 *3^2}=0 \\=>b={a*3*\sqrt3 \over 4}$

Thanks & Regards, Arun Kumar, Btech,IIT Delhi, Askiitians Faculty