ABCD is a square and AB=1 unit .Equilateral triangles AYB and CXD are drawn such that X and Y are inside the square . XY=?

Question

 help to solve thequestion

Answer 1

Draw and label a diagram.

X is √3/2 from AB ⇒ x is 1 - √3/2 from CD

y is √3/2 from CD ⇒ y is 1 - √3/2 from AB

XY = 1 - (1 - √3/2) - (1 - √3/2)

 

 

Answer 2

After drawing the square and the 2 equilateral triangles, draw a line through XY such that the line intersects AB at H and CD at K

 

Since AYB and CXD are equilateral triangles with side 1,

YH = XK = √3/2, so that

YK = XH = 1−√3/2

 

XY = 1 − YK - XH

     = 1 − 2(1−√3/2)

     = √3 − 1