Equilateral triangle

A square is inscribed into an equilateral triangle with a side of 10 cm. Calculate the length of the square side.

Correct result:

b =  4.641 cm

Solution:

a=10 cm h=a2(a/2)2=102(10/2)2=5 3 cm8.6603 cm  tan(60)=b/x a=2x+b  tan(60) (ab)/2=b  a/2 tan(60)=b(1+tan(60)/2)   b=a2 tan601+tan60/2=tanπ/3=4.641=9719π/6579=4.641 cm



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