Question

a man walks around a rectangular park whose perimeter is equal to the perimeter of square with area 9241msq .If he walks with speed 4.5km/hr ,in how much time will he complete one round
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Answer 1

Answer :-

Given :-

Perimeter of the rectangular park = Perimeter of the square

Area of the square = 9241 m²

Speed = 4.5 km/hr

Required to find :-

• Time taken to complete 1 round ?

Formulae used :-

$\large{\boxed{\rm{ Area \; of \; a \; square = side \times side }}}$

$\large{\boxed{\rm{ Perimeter \; of \; a \; square = 4 \times side }}}$

$\large{\boxed{\rm{ Time = \dfrac{Distance}{Speed }}}}$

Solution :-

Area of the square = 9241 m²

But,

Let the side be " x " m

So,

using the formula,

$\large{\boxed{\rm{ Area \; of \; a \; square = side \times side }}}$

9241 = X x X

x² = 9241

x = √9241

x = 96.13 - - -

x = 96.13 meters ( approximately)

Hence,

Using the formula,

$\large{\boxed{\rm{ Perimeter \; of \; a \; square = 4 \times side }}}$

So,

Perimeter of the square = 4 x 96.13

perimeter of the square = 384.5 meters

However it is given that ,

Perimeter of the rectangle park = Perimeter of the square

So,

Perimeter of the rectangular park = 384.5 meters

Since,

The distance covered by man in 1 round = Perimeter of the reactangular park

So,

Distance travelled by the man = 384.5 meters

Speed = 4.5 km/hr

Here we need to convert the speed from km/hr into m/s

So,

1 km/hr = 5/18 m/s

So,

4.5 km/hr = ? m/s

=> 4.5 x 5/18

=> 5/4 m/s

=> Speed of the man = 5/4 m/s

Using the formula,

$\large{\boxed{\rm{ Time = \dfrac{Distance}{Speed }}}}$

So,

$\righatrrow{\tt{ Time = \dfrac{ 384.5 }{ \dfrac{5}{4}}}}$

$\rightarrow{\tt{ Time = \dfrac{384.5 \times 4 }{ 5 } }}$

$\rightarrow{\tt{ Time = \dfrac{ 1538}{ 5 }}}$

$\rightarrow{\tt{ Time = 307.6 \; seconds }}$

Therefore,

Time taken by the man to make 1 round = 307.6 seconds ( approximately )