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Calculate the length of a side of the equilateral triangle with an area of 50cm2.

Correct result:

a =  10.746 cm

Solution:

S=50 cm2  S=ah/2 h=3/2 a  S=a2 3/4 a=4⋅ S/3=4⋅ 50/3=10.746 cmS=50 \ \text{cm}^2 \ \\ \ \\ S=ah/2 \ \\ h=\sqrt{ 3 }/2 \ a \ \\ \ \\ S=a^2 \ \sqrt{ 3 }/4 \ \\ a=\sqrt{ 4 \cdot \ S / \sqrt{ 3 } }=\sqrt{ 4 \cdot \ 50 / \sqrt{ 3 } }=10.746 \ \text{cm}

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