Question

the area of a rectangular field is 3584 sqm and its lenght is 64 m ,a boy runs around the field at the rate of 6kmhr .how long will he take to go 5 times aroun it

Answer 1

$\begin{gathered}\begin{gathered}\bf Given -  \begin{cases} &\sf{area \: of \: rectangular \: feild \: = 3584 \: {m}^{2} } \\ &\sf{length \: of \: rectangle \: = 64 \: m} \\ &\sf{speed \: = 6 \: km \: per \: hour} \\ &\sf{number \: of \: turns \: = \: 5} \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\bf  To \:  Find :-  \begin{cases} &\sf{time \: taken \: to \: complete \: 5 \: rounds}  \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\Large{\bold{\pink{\underline{Formula \: Used \::}}}} \end{gathered}$

$\boxed{\tt \ \: Perimeter \:of\:Rectangle=2(Length + Breadth)}$

$\boxed{\tt \ \: Area\:of\:Rectangle=Length × Breadth}$

$\boxed{\tt \ \: time \: = \dfrac{distance}{speed} }$

$\large\underline\purple{\bold{Solution :- }}$

$\tt \ \: :  ⟼ Area \: of \: rectangular \: feild = 3584 \: {m}^{2}$

$\tt \ \: :  ⟼ length \: of \: rectangular \: feild \: = 64 \: m$

$\tt \ \: :  ⟼ Area\:of\:Rectangle=Length × Breadth$

$\tt \ \: :  ⟼ 3584 = 64 \times Breadth$

$\tt\implies \: Breadth = \dfrac{3584}{64} = 56 \: m$

☆ Now, Distance covered in one round is equal to perimeter of Rectangular field.

$\tt \:  Distance \: covered \: in \: 1 \: round \: = 2(Length + Breadth)$

$\tt\implies \:Distance \: covered \: in \: 1 \: round \: = 2(64 + 56)$

$\tt\implies \:Distance \: covered \: in \: 1 \: round = \: 2 \times 120 = 240m$

$\tt\implies \:Distance \: covered \: in \: 5 \: rounds = 240 \times 5 = 1200 \: m$

$\tt\implies \:Distance \: covered = 1200 \: m = 1.2 \: km$

$\tt \ \: :  ⟼ Speed \: of \: boy \: = \: 6 \: km \: per \: hour$

$\tt\implies \:Time \: taken \: = \dfrac{1.2}{6} = \dfrac{12}{60} = \dfrac{1}{5} \: hours$

$\tt\implies \:Time \: taken \: = \dfrac{1}{5} \times 60 = 12 \: minutes$