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

Explanation

Area of equilateral triangle=`sqrt3/4a^3`

Area of square`=side^2`

`S=sqrt3/4(x/3)^2+((20-x)/4)^2`

`(dS)/(dx)=sqrt3/4*1/3^2*2x+2((20-x)/4)*-1/4=0`

`(2sqrt3)/(36)x-1/8(20-x)=0`

`25/36x-20/8+x/8=0`

`(45x+9)x/72=20/8`

`x=180/(4sqrt3+9)`

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