The side of a triangular plot are in the ratio of 3:5:7 and it’s perimeter is 300. find its area.
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1. Given : ↴

   [tex] \sf \: The \: sides \: of \: a \: triangular \: plot \: are \: in \: the \: ratio \: of \: 3 :5 : 7. [/tex]

   [tex] \sf \: It’s \: perimeter \: is \: 300 \: m. [/tex]

   [tex] \sf \underline\red{{\bf To \: find} : }[/tex]↴

   [tex] \sf \: We \: have \: to \: find \: the \: area \: of \: the \: \triangle[/tex]

   [tex] \underline\red{{\bf So, \:Let’s \:find \:it }:}[/tex] ↴

   [tex] \sf \: Let \: us \: suppose \: that \: the \: sides \: are \: 3x, \: 5x, \: 7x.[/tex]

   [tex] \sf \: Here \: it \: is \: given \: that \: the \: Perimeter \: of \: \triangle \: is \: 300.[/tex]

   [tex] \sf \: So, \: 3x \: + \: 5x \: + \: 7x \: = \: 300 [/tex]

   [tex] \sf \: \rightarrow \: 15x \: = \: 300 [/tex]

   [tex] \sf \: \rightarrow \: x \: = \: \dfrac{300}{15} [/tex]

   [tex] \sf \longrightarrow \: So, \: x = \: \: 20[/tex]

   [tex] \sf \: Therefore, [/tex]

   [tex] \sf \longrightarrow \: 3x \: = \: 3 \: \times \: 20 \: = \: 60 [/tex]

   [tex] \sf \longrightarrow \: 5x \: = \: 5 \: \times \: 20 \: = \: 100[/tex]

   [tex] \sf \longrightarrow \: 7x \: = \: 7 \: \times \: 20 \: = \: 140[/tex]

   [tex] \sf \: So, \: the \: Sides \: of \: the \: \triangle \: are \: 60, \: 100 \: and \: 140. [/tex]

   [tex] \sf \: \underline{Now, \: By \: using \: Heron’s \: formula \: we \: will \: find \: the \: Area. }[/tex]

   [tex] \sf \: Semi \: perimeter \: of \: a \: \triangle \: :[/tex] ↴

   [tex]\sf{\rightarrow\dfrac{60+100+140}{2}}[/tex]

   [tex] \sf \: \red{Area \: of \: \triangle \: : }[/tex] ↴

   [tex]\sf{\rightarrow \sqrt{s(s-a)(s-b)(s-c)}}[/tex]

   [tex]\sf{\rightarrow \sqrt{150(150-60)(150-100)(150-140)}}[/tex]

   [tex]\sf{\rightarrow \sqrt{150\times 90\times 50\times 10}}[/tex]

   [tex]\sf{\rightarrow \sqrt{3\times 50\times 3\times 30\times 50\times 10}}[/tex]

   [tex]\sf{\rightarrow \sqrt{3\times 3\times 50\times 50\times 10\times 10\times 3}}[/tex]

   [tex]\sf{\rightarrow 3\times 50\times 10\sqrt{3}}[/tex]

   [tex]\sf{\rightarrow 1500\times 10\sqrt{3} \: m^{2} }[/tex]

   [tex] \sf \: \purple {Therefore \: area \: of \: the\: \triangle \: = {1500\times 10\sqrt{3} \: m^{2}} }[/tex]

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