Question

A rectangular field has its length and breadth in the ratio of 5 : 4 respectively. A man riding a

bicycle, completes one lap of this field along its perimeter at the speed of 9 km./hr. in 3 minutes

and 36 seconds. What is the area of the field ?​

Answer 1

Hope this helps.......

Answer 2

The area of the field is 18000 square meters .

Explanation:

Given : A rectangular field has its length and breadth in the ratio of 5 : 4 respectively.

Let length be 5x and width be 4x.

Perimeter = 2(l+w) = 2(5x+4x)=18x    (1)

Speed of bicycle= 9 km./hr. $=\dfrac{9\times1000}{3600}= 2.5\ m/s$

[∵ 1 hour = 3600 seconds & 1 km = 1000 meters]

Time taken to complete one lap = 3 minutes and 36 seconds

= 3(60) seconds +36 seconds   [∵ 1 minute = 60 seconds]

= 180+36 seconds

=  216 seconds

Since , Distance = Speed x Time

Distance covered in one lap =2.5 x 216 = 540 meters

∴ Perimeter = 540 meters

From (1)  18x = 540

x= 30   [Divide both sides by 18]

So , length =5 (30)=150 m

width = 4(30)=120 m

Area of rectangular field = l x w = 150 x 120 =18000 square meters.

Hence, the area of the field is 18000 square meters .

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