Question

The ratio of length and breadth of a rectangular park is 4:2. If a cat running along the boundary of the park at the speed of 18 kmph completes one round in 10 minutes, find the area of the park in square meters. एक आयताकार पार्क की लंबाई और चौड़ाई का अनुपात 4: 2 है। यदि 18 किमी प्रति घंटे की गति से पार्क की सीमा के साथ चलने वाली बिल्ली 10 मिनट में एक चक्कर पूरा करती है, तो पार्क का क्षेत्रफल वर्ग मीटर में ढूंढें।

Answer 1

Your Answer :

Given :

Ratio of length and breadth of a rectangular park = 4:2

Speed of the cat = 18km/hr

Convert the speed from kmph into mps

So , to do that multiply it with 5 and divide it with 18.

$18kmph = 18 \times \frac{5}{18} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 5 \: mps$

Time taken = 10 minutes

Convert this minutes into seconds by multiplying it with 60

10 x 60

= 600 seconds

Required to find :

1. Area of the rectangular park

Solution :

To Solve this question consider the second part of the question that is

A cat is running along the boundary of the park at the speed of 5m/s [ 18km/hr] to complete 1 round in 10 minutes.

Therefore, using the most familiar formula ;

$distance \: = speed \times time$

So, by substituting the values and performing calculations we get

distance = 5m/sec x 600 seconds

= 3000 meters.

Now,

Consider the first part of the question that is ratio of length and breadth of a rectangle is 4:2

Then,

Let the length be 4x

breadth be 2x

But actually,

We have to conclude that

Distance travelled by the cat = perimeter of the rectangle.

Therefore,

perimeter of the rectangular park = 3000 meters.

But according to problem

2(length x breadth ) = 3000 meters

2( 4x + 2x ) = 3000

2(6x) = 3000

12x = 3000

x = 3000/12

x = 250 meters.

From the above we will get that,

length = 4x = 4(250) = 1000 meters

breadth = 2x = 2(250) = 500 meters

Therefore,

The dimensions of the park are 1000 meters x 500 meters

Hence ,

We can find the area of the rectangle using the formula,

Area of the rectangle = length x breadth

= 1000 x 500

= 5,00,000 m^2

Therefore,

Area of the park in meter square is 5,00,000m^2