Question

Hello Good Evening Friends ❤️❤️❤️

A path 3m wide runs around the inside of a square park of side 60m. Find the area of the path.​

Answer 1

Answer:

✩ DIAGRAM :

$\setlength{\unitlength}{1.45mm}\begin{picture}(8,2)\linethickness{0.4mm}\multiput(8,1)(0,30){2}{\line(2,0){30}}\multiput(8,1)(30,0){2}{\line(0,2){30}}\multiput(11,4)(0,24){2}{\line(2,0){24}}\multiput(11,4)(24,0){2}{\line(0,2){24}}\put(40,15){\sf 60 m}\put(20,6){\sf 54 m}\put(35,1){\line(0,2){3}}\put(35,4){\line(2,0){3}}\qbezier(36,2)(50,2)(50,6)\put(48,7){\sf3 m Width}\end{picture}$

⠀⠀⠀$\rule{160}{1}$

☢ Concept to Understand : Side of Square Park is 60 m , when we will measure the Side of Inside of Park leaving the Path. We have to Leave Uniform Width of Path from Both Sides.

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⠀⠀⠀✩ Outer Side of Park = 60 m

⠀⠀⠀✩ Inner Side = 60 - (3 + 3) = 54 m

⠀

☯ $\underline{\boldsymbol{According\: to \:the\: Question :}}$

$:\implies\sf Area_{(Path)}=Outer\:Square_{(Area)}-Inner\:Square_{(Area)}\\\\\\:\implies\sf Area_{(Path)}=(Outer\:Side)^2-(Inner\: Side)^2\\\\\\:\implies\sf Area_{(Path)}=(60)^2-(54)^2\\\\\\:\implies\sf Area_{(Path)} = (60 + 54)(60 - 54)\\\\\\:\implies\sf Area_{(Path)} = 114 \times 6\\\\\\:\implies\underline{\boxed{\sf Area_{(Path)} = 684\: {m}^{2} }}$

⠀

$\therefore\:\underline{\textsf{Hence, Area of Path will be \textbf{684 m ^\text2 }}}.$