1.

5. Find the area of a triangular field whose sides are 91 m, 98 m and 105 min length. Find the height corresponding to the longest side.​

Answer»

Given: Sides of triangular field are 91 m, 98 m and 105 m.

To find: The height CORRESPONDING to the longest side?

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀⠀

\underline{\bigstar\:\boldsymbol{Using\: Heron's\:Formula\::}}\\ \\

\star\;{\boxed{\sf{\pink{Area_{\;(triangle)} = \sqrt{s(s - a)(s - b)(s - c)}}}}}\\ \\

:\implies\sf s = semi - perimeter\\ \\

:\implies\sf s = \dfrac{a + b + c}{2}\\ \\

:\implies\sf s = \dfrac{91 + 98 + 105}{2}\\ \\

:\implies\sf s = \cancel{ \dfrac{294}{2}}\\ \\

:\implies{\underline{\boxed{\frak{\purple{s = 147\:m}}}}}\;\bigstar

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀⠀

\bf{\dag}\;{\underline{\frak{Now,\:Putting\:values\:in\:formula,}}}\\ \\

:\implies\sf Area_{\;(field)} = \sqrt{147(147 - 91)(147 - 98)(147 - 105)}\\ \\

:\implies\sf Area_{\;(field)} = \sqrt{147 \times 56 \times 49 \times 42}\\ \\

:\implies\sf Area_{\;(field)} = \sqrt{16941456}\\ \\

:\implies{\underline{\boxed{\frak{\purple{Area_{\;(field)} = 4116\:m^2}}}}}\;\bigstar\\ \\

\therefore\:{\underline{\sf{Area\:of\:triangular\:field\:is\: \bf{4116\:m^2}.}}}

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀⠀

☯ Let's Consider H as the height corresponding to the longest side.

⠀⠀⠀⠀

Here,

  • 105 m is the longest side = Base

⠀⠀⠀⠀

\dag\;{\underline{\frak{As\;we\;know\;that,}}}\\ \\

\star\;{\boxed{\sf{\pink{Area_{\;(triangle)} = \dfrac{1}{2} \times base \times height}}}}\\ \\

:\implies\sf \dfrac{1}{2} \times 105 \times h = 4116\\ \\

:\implies\sf 105 \times h = 4116 \times 2\\ \\

:\implies\sf 105 \times h = 8232\\ \\

:\implies\sf h = \cancel{ \dfrac{8232}{105}}\\ \\

:\implies{\underline{\boxed{\frak{\purple{Area_{\;(field)} = 78.4\:m}}}}}\;\bigstar\\ \\

\therefore\:{\underline{\sf{Hence,\:the\:height\: corresponding\:to\:the\;longest\: side\:is\; {\textsf{\textbf{78.4\:m}}}.}}}


Discussion

No Comment Found

Related InterviewSolutions