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A wire of length 36cm is cut into the tw...

A wire of length 36cm is cut into the two pieces, one of the pieces is turned in the form of a square and other in form of an equilateral triangle. Find the length of each piece so that the sum of the areas of the two be minimum

Text Solution

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`4a = x`
`a=x/4`
in trianlge, `3b = 36-x`
`b= (36-x)/3 = 12-x/3`
now,`A= a^2 + sqrt3/4b^2`
`A= x^2/16 + sqrt3/4(12-x/3)^2`
`A= x^2/16 + sqrt3/4 (12^2 + x^2/9 - 2 * 12*x/3)`
`A= x^2/16 + sqrt3/4 (12^2 + x^2/9 - 8x)`
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