Sick square 1

Geometry Level 2

In the diagram, D , T , D, T, and S S are three vertices of the regular hexagon with side length 6.

If A B C D ABCD is a square drawn such that A D AD and B C BC are parallel to S T ST with S S on A B , AB, what is the side length of the square?


The answer is 9.

Ajay Sambhriya by Ajay Sambhriya , 27, India

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1 solution

sin ⁡ 30 = T U 6 \sin 30 = \dfrac{TU}{6}

T U = 6 sin ⁡ 30 TU = 6 \sin 30

The side length of the square is

S U = 6 + T U = 6 + 6 sin ⁡ 30 = 9 SU = 6 + TU = 6 + 6 \sin 30 = \boxed{9}

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