Two congruent squares are placed in an equilateral triangle of side length 8. Find the side length of each square.
+36916 x = square side length
Triangle in bottom right has base length of (8 - 2x)/2
Tan 60 = opp/adj = x / (8-2x)/2 = 2x/(8-2x) tan 60 = sqrt 3
sqrt 3 = 2x/(8-2x)
8 sqrt 3 - 2x sqrt 3 = 2x
8 sqrt 3 = 2x + 2x sqrt 3
8 sqrt 3 = x (2+ 2 sqrt 3)
( 8 sqrt 3) / (2+2 sqrt 3) = x
rationalize the denominator to get
x = 6- 2 sqrt 3
+36916 x = square side length
Triangle in bottom right has base length of (8 - 2x)/2
Tan 60 = opp/adj = x / (8-2x)/2 = 2x/(8-2x) tan 60 = sqrt 3
sqrt 3 = 2x/(8-2x)
8 sqrt 3 - 2x sqrt 3 = 2x
8 sqrt 3 = 2x + 2x sqrt 3
8 sqrt 3 = x (2+ 2 sqrt 3)
( 8 sqrt 3) / (2+2 sqrt 3) = x
rationalize the denominator to get
x = 6- 2 sqrt 3
