Solve this:

Dear Student,





$$\begin{gathered} Given : Perimeter of the farmer\text{'}s field=300m and it\text{'}s sides are in the ratio of 5:12:13. \\ To Determine : The length of the perpendicular from the opposite vertex to the longest side. \\ solution : Let\text{'}s name the triangular field as ABC such that the sides AB, AC and BC are in the ratio of 5:12:13. \\ Also, AD id the length of perpendicular to the longest side BC \\ so, let the sides AB be 5k, AC be 12k and BC be 13k \\ And as it is given that the perimeter of the field=300m \\ \Rightarrow 5k+12k+13k=300 \\ \Rightarrow 30k=300 \\ \Rightarrow k=\frac{300}{30} \\ \Rightarrow k=10 \\ So, side AB=5k=5\times 10=50m \\ side AC=12k=12\times 10=120m \\ and side BC=13k=13\times 10=130m \\ So, Area of △ABC=\sqrt{s(s-a)(s-b)(s-c)}=\frac{1}{2}\times base\times height \\ here s=semi perimeter=\frac{300}{2}=150 \\ \Rightarrow \sqrt{150(150-130)(150-120)(150-50)}=\frac{1}{2}\times BC\times AD \\ \Rightarrow \sqrt{150\times 20\times 30\times 100}=\frac{1}{2}\times 130\times AD \\ \Rightarrow \sqrt{90000\times 100}=65\times AD \\ \Rightarrow 300\times 10=65\times AD \\ \Rightarrow AD=\frac{3000}{65}=\frac{600}{13}=46.154 m \\ Hence, length of the perpendicular from the opposite vertex to the longest side 46.154 m. \end{gathered}$$
Hope this information will clear your doubts about topic.

If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible.

Keep posting!!

Regards