Question

the area of a rectangular field is 3584 m2 and its length is 64m. A boy runs around the feild at the rate of 6 km/hrs . how long will he take to go 5 times around it​

Answer 1

Given :-

Area of the rectangular field = 3584 m²

Length of the rectangular field = 64 m

A boy runs around the field at the rate of 6 km/hr.

To Find :-

Time taken to go 5 times around the rectangular field.

Analysis :-

Firstly, find the breadth of the rectangular field by substituting the given values in it's respective formula.

Then find the perimeter of the rectangular field accordingly.

Multiply the perimeter by 5 since the boy ran 5 times around it.

Convert the rate of running to m/s.

Then time taken to cover the distance accordingly.

Solution :-

We know that,

• l = Length
• b = Breadth
• a = Area
• p = Perimeter

By the formula,

$\underline{\boxed{\sf Area \ of \ rectangle=Length \times Breadth}}$

Let the breadth be 'x'.

Given that,

Area (a) = 3584 m²

Length (l) = 64 m

Substituting their values,

3584 = 64 × x

x = 3584/64

x = 56 m

Therefore, the breadth of the rectangular field is 56 m.

By the formula,

$\underline{\boxed{\sf Perimeter \ of \ rectangle=2(Length + Breadth)}}$

Given that,

Length (l) = 64 m

Breadth (b) = 56 m

Substituting their values,

Perimeter = 2(64 + 56)

= 2(120)

= 240 m

Therefore, the perimeter of the rectangle is 240 m.

Given that, he take to go 5 times around the rectangular field.

240 × 5 = 1200 m

Speed of boy = 6 km/h

By converting,

6 × 18/5

= 5/3 m/s

According to the question,

Time taken to cover 1200 m distance = 1200/5 × 3

Time = 240 × 3

Time = 720/60

Time = 12 min

Therefore, 12 min are required to complete 5 rounds of field.