Question

the area of a rectangular field is 3584 m and its lenght is 64 m . a boy runs around the field at the rate of 6 km/h . how long will it take to go 5 times around it

Answer 1

Answer:

Area of Rectangle is: 3584 = L×W

3584 = 64 × W

W=56m

perimeter = 64+56+64+56 = 240m

total distance = 240×5 = 1200m

speed is 6km/h

hence 6000 m in 60 minutes

then for 1200 m how many minutes

Answer will be 12 minutes or 1/5 hour

Answer 2

Appropriate Question :-

The area of a rectangular field is 3584 sq. m and its length is 64 m . A boy runs around the field at the rate of 6 km/h . How long will it take to go 5 times around it?

$\large\underline{\sf{Solution-}}$

Given that,

Area of rectangular field = 3584 sq. m

Length of rectangular field = 64 m

We know,

$\rm \: Area = Length \times Breadth$

$\rm \: 3584 = 64 \times Breadth$

$\rm \: Breadth = \dfrac{3584}{64}$

$\rm\implies \:Breadth \: = \: 56 \: m$

Now, we have to find the perimeter of rectangular field.

So,

$\rm \: Perimeter = 2(Length + Breadth)$

$\rm \: Perimeter = 2(56 + 64)$

$\rm \: Perimeter = 2 \times 120$

$\rm\implies \:Perimeter = 240 \: m$

It means,

Distance covered by boy in one round = 240 m

Distance covered by boy in 5 rounds = 240 × 5 = 1200 m

Now, it is given that speed of boy is 6 km per hour.

Speed of boy = 6 × 5/18 = 5/3 m per sec.

We know,

$\rm \: Time = \dfrac{Distance}{Speed}$

$\rm \: Time = 1200 \times \dfrac{3}{5}$

$\rm \: Time = 240 \times 3$

$\rm \: Time = 720 \: sec$

$\rm \: Time = 12 \: minutes$

So,

$\rm\implies \:\rm \: Time \: taken \: = 12 \: minutes$

$\rule{190pt}{2pt}$

Additional Information :-

$\begin{gathered}\begin{gathered}\boxed{\begin {array}{cc}\\ \dag\quad \Large\underline{\bf Formulas\:of\:Areas:-}\\ \\ \star\sf Square=(side)^2\\ \\ \star\sf Rectangle=Length\times Breadth \\\\ \star\sf Triangle=\dfrac{1}{2}\times Base\times Height \\\\ \star \sf Scalene\triangle=\sqrt {s (s-a)(s-b)(s-c)}\\ \\ \star \sf Rhombus =\dfrac {1}{2}\times d_1\times d_2 \\\\ \star\sf Rhombus =\:\dfrac {1}{2}d\sqrt {4a^2-d^2}\\ \\ \star\sf Parallelogram =Base\times Height\\\\ \star\sf Trapezium =\dfrac {1}{2}(a+b)\times Height \\ \\ \star\sf Equilateral\:Triangle=\dfrac {\sqrt{3}}{4}(side)^2\end {array}}\end{gathered}\end{gathered}$