An equilateral

An equilateral triangle is inscribed in a square of side 1 unit long so that it has one common vertex with the square. What is the area of the inscribed triangle?

Correct answer:

S =  0.4641

Step-by-step explanation:

a2=12+x2 a2=(1x)2+(1x)2  1+x2=(1x)2+(1x)2  12+x2=(1x)2+(1x)2  x2+4x1=0 x24x+1=0  a=1;b=4;c=1 D=b24ac=42411=12 D>0  x1,2=b±D2a=4±122=4±232 x1,2=2±1.73205080757 x1=3.73205080757 x2=0.267949192431   Factored form of the equation:  (x3.73205080757)(x0.267949192431)=0  0<x<1 x=x2=0.26790.2679  a=1+x2=1+0.267921.0353  S=34 a2=34 1.03532=0.4641

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