Question

the length of A rectangular field is twice it's breadth. A man jogged around it 5times and covered A distance of 3km. what is the length of field



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Answer 1

AnswEr :

Let the Breadth be x metres and, Length be 2x metres of Rectangluar Field.

⋆ Refrence of Image is in the Diagram :

$\setlength{\unitlength}{1.5cm}\begin{picture}(8,2)\thicklines\put(7.7,3){\large{A}}\put(7.3,2){\mathsf{\large{x m}}}\put(7.7,1){\large{B}}\put(9.2,0.7){\matsf{\large{2x m}}}\put(11.1,1){\large{C}}\put(8,1){\line(1,0){3}}\put(8,1){\line(0,2){2}}\put(11,1){\line(0,3){2}}\put(8,3){\line(3,0){3}}\put(11.1,3){\large{D}}\end{picture}$

$\rule{150}{1}$

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

$:\implies\tt Distance\:Covered = Perimeter \times Times\: of\:Field\\\\\\:\implies\tt 3 \:Km = 2(Length + Breadth) \times 5\\\\\\:\implies\tt (3 \times 1000) \: m = 2(2x + x) \times 5\\\\\\:\implies\tt 3000 = 2(3x) \times 5\\\\\\:\implies\tt 3000= 6x \times5\\\\\\:\implies\tt 3000= 30x\\\\\\:\implies\tt \dfrac{3000}{30}=x\\\\\\:\implies\tt x = 100 \:m$

$\rule{200}{2}$

$\underline{\bigstar\:\textsf{Length of Rectangluar Field :}}$

$\longrightarrow\tt Length = 2x\\\\\\\longrightarrow\tt Length =2(100 \:m)\\\\\\\longrightarrow\boxed{\tt Length =200 \:m}$

⠀

$\therefore\:\underline{\textsf{Length of Rectangluar Field is \textbf{200 m.}}}$

Answer 2

$\bf{\Huge{\boxed{\tt{\pink{ANSWER\::}}}}}$

$\bf{\Large{\underline{\underline{\bf{Given\::}}}}}$

The length of a rectangular field is twice it's breadth. A man jogged around it 5 times and covered a distance of 3 km.

$\bf{\Large{\underline{\underline{\bf{To\:Find\::}}}}}$

The length of the field.

$\bf{\Large{\underline{\underline{\tt{\red{Explanation\::}}}}}}$

We know that formula of the perimeter of rectangle:

$\leadsto\sf{\large{Perimeter\:=\:2(Length*Breadth)}}$

$\bf{We\:have}\begin{cases}\sf{Length\:of\:rectangle\:(L)\:=\:2R}\\ \sf{Breadth\:of\:rectangle\:(B)\:=\:R}\\ \sf{Distance\:Covered\:=\:3km\:=\:3000m}\\ \sf{A\:man\:Jogged\:around\:5\:times}\end{cases}}$

A/q

$\hookrightarrow\:\sf{Perimeter\:=\:2(L+B)}\\\\\\\\\hookrightarrow\:\sf{Perimeter\:=\:5*2(L+B)}\\\\\\\\\hookrightarrow\:\sf{Periemeter\:=\:10(2R+R)}\\\\\\\\\hookrightarrow\:\sf{Perimeter\:=\:10(3R)}\\\\\\\\\hookrightarrow\:\sf{Perimeter\:=\:30R}$

__________________________________________

Perimeter of the field = Distance covered by man.

$\leadsto\sf{30R\:=\:3000}\\\\\\\\\leadsto\sf{R\:=\:\cancel{\dfrac{3000}{30} }}\\\\\\\\\leadsto\sf{\red{R\:=\:100m}}$

Thus,

⇒ The length of the field is 2R

⇒ The length of the field is 2(100)m = 200m.