Three parallels

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

Correct answer:

v =  7 m

Step-by-step explanation:

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  = (82  32 + 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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