Three parallels

The vertices of an equilateral triangle lie on 3 different parallel lines. The middle line is 5 m and 3 m distant from the end lines. Calculate the height of this triangle.

Correct result:

v =  7 m

Solution:

a2=32+x2 a2=52+y2 a2=82+(yx)2  32+x2=52+y2 32+x2=82+(yx)2  32+x2=82+y22xy+x2 32=82+y22xy  x=(8232+y2)/(2y)  y=11/36.3509 m  x=(8232+y2)/(2y)=(8232+6.35092)/(2 6.3509)7.5056 m  a=32+x2=32+7.505628.0829 m  v2=a2(a/2)2  v=a2(a/2)2=8.08292(8.0829/2)2=7 m



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