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Geometry Level pending

ABCD is a square. Given that AB is 6 cm and triangles ABF and CED are equilateral. Find the length of EF exactly. And then give your answer to 4.sf.


The answer is 4.392.

Syed Hamza Khalid by Syed Hamza Khalid , 17, France

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1 solution

Consider right △ F G B \triangle FGB . Applying the theorem of Pythagoras, we have, G F = 6 2 − 3 2 = 3 3 GF=\sqrt{6^2-3^2}=3\sqrt{3} . Therefore the length of E F EF to four significant figures is

E F = 2 ( 3 3 ) − 6 ≈ 4.392 EF=2(3\sqrt{3})-6\approx \color{#D61F06}\boxed{4.392}

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