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Given : Perimeter of the farmer's field=300m and it's sides are in the ratio of 5:12:13.To Determine : The length of the perpendicular from the opposite vertex to the longest side.solution : Let's name the triangular field as ABC such that the sides AB, AC and BC are in the ratio of 5:12:13.Also, AD id the length of perpendicular to the longest side BCso, let the sides AB be 5k, AC be 12k and BC be 13k And as it is given that the perimeter of the field=300m5k+12k+13k=30030k=300k=30030k=10So, side AB=5k=5×10=50mside AC=12k=12×10=120mand side BC=13k=13×10=130mSo, Area of ABC=s(s-a)(s-b)(s-c)=12×base×heighthere s=semi perimeter=3002=150150(150-130)(150-120)(150-50)=12×BC×AD150×20×30×100=12×130×AD90000×100=65×AD300×10=65×ADAD=300065=60013=46.154 mHence, length of the perpendicular from the opposite vertex to the longest side 46.154 m.
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