A rectangular lawn is 15 metre long and 9 metre wide it has a path 1.5

1.	A rectangular lawn is 15 metre long and 9 metre wide it has a path 1.5 metre wide all around it find the area of the path(Answer = 81m square)Explain
Answer» ANSWER : ⋆ REFERENCE of IMAGE is in the DIAGRAM : $\setlength{\unitlength}{1.5cm}\begin{picture}(8,2)\thicklines\put(7.3,2){\large{12 m}}\put(9.2,0.7){\large{18 m}}\put(8,1){\line(1,0){3}}\put(8,1){\line(0,2){2}}\put(11,1){\line(0,3){2}}\put(8,3){\line(3,0){3}}\setlength{\unitlength}{1.5cm}\put(8.4,2){\large{9 m}}\put(9.2,1.4){\large{15 m}}\put(8.3,1.26){\line(1,0){2.4}}\put(8.3,1.25){\line(0,2){1.5}}\put(10.7,1.25){\line(0,3){1.5}}\put(8.3,2.74){\line(3,0){2.4}}\put(8.3,1){\line(0,3){0.3}}\put(8,1.26){\line(3,0){0.3}}\put(8,1.1){\small{1.5}}\end{picture}$ $\rule{150}{1}$ $\bullet\:\textsf{Length of Lawn ( l ) = 15 m}\\\\\bullet\:\textsf{Breadth of Lawn ( b ) = 9 m}\\\\\bullet\:\textsf{Outer Length ( L ) = [15 + 2(1.5)] m}\\\textsf{\qquad\qquad\qquad\qquad\quad\:= [15 + 3] m = 18 m}\\\\\bullet\:\textsf{Outer Breadth ( B ) = [9 + 2(1.5)] m}\\\textsf{\qquad\qquad\qquad\qquad\qquad\!= [9 + 3] m = 12 m}$ $\rule{200}{2}$ $\underline{\bigstar\:\textsf{According to the Question Now :}}$ $:\implies\texttt{Area of Path = Outer Area - Inner Area}\\\\\\:\implies\tt Area\:of\:Path = (Length \times Breadth)-(length \times breadth)\\\\\\:\implies\tt Area\:of\:Path = (L \times B)- (l \times b)\\\\\\:\implies\tt Area\:of\:Path =(18m\times12m)-(15m\times 9m)\\\\\\:\implies\tt Area\:of\:Path =216 m^2- 135 m^2\\\\\\:\implies\boxed{\tt Area\:of\:Path = 81\:m^2}$ ⠀ $\therefore\:\underline{\textsf{Area of the Path around Lawn is \textbf{81 m$^2$.}}}$

A rectangular lawn is 15 metre long and 9 metre wide it has a path 1.5 metre wide all around it find the area of the path(Answer = 81m square)Explain

Answer»

ANSWER :

⋆ REFERENCE of IMAGE is in the DIAGRAM :

$\setlength{\unitlength}{1.5cm}\begin{picture}(8,2)\thicklines\put(7.3,2){\large{12 m}}\put(9.2,0.7){\large{18 m}}\put(8,1){\line(1,0){3}}\put(8,1){\line(0,2){2}}\put(11,1){\line(0,3){2}}\put(8,3){\line(3,0){3}}\setlength{\unitlength}{1.5cm}\put(8.4,2){\large{9 m}}\put(9.2,1.4){\large{15 m}}\put(8.3,1.26){\line(1,0){2.4}}\put(8.3,1.25){\line(0,2){1.5}}\put(10.7,1.25){\line(0,3){1.5}}\put(8.3,2.74){\line(3,0){2.4}}\put(8.3,1){\line(0,3){0.3}}\put(8,1.26){\line(3,0){0.3}}\put(8,1.1){\small{1.5}}\end{picture}$

$\rule{150}{1}$

$\bullet\:\textsf{Length of Lawn ( l ) = 15 m}\\\\\bullet\:\textsf{Breadth of Lawn ( b ) = 9 m}\\\\\bullet\:\textsf{Outer Length ( L ) = [15 + 2(1.5)] m}\\\textsf{\qquad\qquad\qquad\qquad\quad\:= [15 + 3] m = 18 m}\\\\\bullet\:\textsf{Outer Breadth ( B ) = [9 + 2(1.5)] m}\\\textsf{\qquad\qquad\qquad\qquad\qquad\!= [9 + 3] m = 12 m}$

$\rule{200}{2}$

$\underline{\bigstar\:\textsf{According to the Question Now :}}$

$:\implies\texttt{Area of Path = Outer Area - Inner Area}\\\\\\:\implies\tt Area\:of\:Path = (Length \times Breadth)-(length \times breadth)\\\\\\:\implies\tt Area\:of\:Path = (L \times B)- (l \times b)\\\\\\:\implies\tt Area\:of\:Path =(18m\times12m)-(15m\times 9m)\\\\\\:\implies\tt Area\:of\:Path =216 m^2- 135 m^2\\\\\\:\implies\boxed{\tt Area\:of\:Path = 81\:m^2}$

⠀

$\therefore\:\underline{\textsf{Area of the Path around Lawn is \textbf{81 m$^2$.}}}$