Question

a ground in 100m * 60m . A path outside it is present there it's area is equal to 3/5 of the area of the ground find its breadth​

Answer 1

AnswEr :

⋆ Refrence of Image is in the Diagram :

$\setlength{\unitlength}{1.5cm}\begin{picture}(8,2)\thicklines\put(11.1,2){\large{(60 + 2x) m}}\put(9,0.7){\large{(100 + 2x) m}}\put(8,1){\line(1,0){3}}\put(8,1){\line(0,2){2}}\put(11,1){\line(0,3){2}}\put(8,3){\line(3,0){3}}\put(8.4,2){\large{60 m}}\put(9.2,1.4){\large{100 m}}\put(8,1.26){\line(1,0){2.7}}\put(8.3,1){\line(0,2){1.76}}\put(10.7,1.25){\line(0,3){1.5}}\put(8.3,2.74){\line(3,0){2.4}}\put(8.1,1.07){\scriptsize{x}}\end{picture}$

⠀

$\star\:\textsf{Let the Width of Path be x.}\\\\\bullet\:\:\textsf{Outside Length = 100 + x + x = (100 + 2x)}\\\bullet\:\:\textsf{Outside Breadth = 60 + x + x = (60 + 2x)}$

$\rule{190}{1}$

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

$:\implies\texttt{Area of Path = (Outer Area) - (Inner Area)}\\\\\\:\implies\tt \dfrac{3}{5}\:of\:Area\:of\:Ground=\lbrack(100+2x) \times (60+2x)\rbrack - \lbrack100 \times 60\rbrack\\\\\\:\implies\tt \dfrac{3}{5} \times (100 \times 60) = \lbrack6000 + 200x + 120x + 4x^{2}\rbrack - 6000\\\\\\:\implies\tt 3 \times 20 \times 60 = 6000 + 320x + 4{x}^{2} - 6000\\\\\\:\implies\tt 3600 = 320x + 4{x}^{2}\\\\\\:\implies\tt 3600 = 4(80x + {x}^{2})\\\\\\:\implies\tt 900 = 80x + {x}^{2}\\\\\\:\implies\tt {x}^{2} + 80x - 900 = 0\\\\\\:\implies\tt {x}^{2} + (90 - 10)x - 900 = 0\\\\\\:\implies\tt {x}^{2} + 90x - 10x - 900 = 0\\\\\\:\implies\tt x(x + 90) - 10(x + 90) = 0\\\\\\:\implies\tt (x - 10)(x + 90) = 0\\\\\\:\implies\tt \green{x = 10} \quad or \quad \red{x = - \:90}$

$\rule{200}{2}$

☢$\:\:\underline{\textsf{Outer Breadth :}}$

$\dashrightarrow\tt\:\: Outer\:Breadth=(60+2x)\:m\\\\\\\dashrightarrow\tt\:\: Outer\:Breadth=(60+2 \times 10)\:m\\\\\\\dashrightarrow \tt\:\: Outer\:Breadth=(60+20)\:m\\\\\\\dashrightarrow\:\: \underline{\boxed{\orange{\tt Outer\:Breadth=80 \:m}}}$

⠀

$\therefore\:\underline{\textsf{Breadth outside of the ground is \textbf{80 m.}}}$