Geodesist

Triangle shaped field (triangle ABC) has side AB = 129 m. path XY is parallel to the side AB which divided triangle ABC into two parts with same area.

What will be the length of the path XY? Help please geodesist ...

Correct result:

|XY| =  91.2 m

Solution:

c=c2=129 m 2S1=S2  S1=c1h12 S2=c2(h1+h2)2  c1h1=c2h1+h2 h1+h2=c2h1c1  2c1h12=c2(h1+h2)2 2c1h1=c2(h1+h2) 2c1h1=c2c2h1c1  2c12h1=c22h1 2c12=c22 c12=c22/2 c1=c2/2=129/2=91.2 m



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