Question

a rectangular field has its length and breadth in the ratio 6:5 respectively. a man riding bicycle complete one lap of the field along its perimeter at the speed of 12 kmph in 1.5m. what is the area of the field?​

Answer 1

Answer:

• Area of the rectangular field is 5467.5 m².

Step-by-step explanation:

Given that:

• A rectangular field has its length and breadth in the ratio 6 : 5.
• A man riding bicycle completes one lap of the field along its perimeter at the speed of 12 km/h in 1.5 minutes.

To Find:

• Area of the field.

Solution:

Converting 12 km/h to m/s:

To convert km/h to m/s we have to divide it by 18/5.

$\sf{\longmapsto12\;km/h=\left(12\div\dfrac{18}{5}\right)m/s}$

$\sf{=\left(12\times\dfrac{5}{18}\right)m/s}}$

Reducing the numbers,

$\sf{=\left(2\times\dfrac{5}{3}\right)m/s}}$

Multiplying the numbers,

$\sf{=\dfrac{10}{3}\;m/s}}$

Dividing the numbers,

$\sf{=3.3\;m/s}}$

Converting 1.5 minutes to seconds:

To convert minutes into seconds we have to multiply it by 60.

$\sf{\longmapsto1.5\;minutes=(1.5\times60)\;seconds}}$

$\sf{=90\;seconds}}$

Finding distance covered by the man:

As we know that,

• Distance = Time × Speed

Substituting the values,

$\sf{\longmapsto(3.3\times90)m}$

$\sf{\longmapsto297\;m}$

Hence,

• Distance covered by the man = 297 m

Therefore,

• Perimeter of the field = 297 m

Let us assume:

• Length and breadth of the field be 6x and 5x respectively.

As we know that:

• Perimeter = 2(length + breadth) units

Substituting the values,

$\sf{\longmapsto297=2(6x+5x)}$

$\sf{\longmapsto297=2\times11x}$

$\sf{\longmapsto297=22x}$

$\sf{\longmapsto\dfrac{297}{22}=x}$

$\sf{\longmapsto13.5=x}$

Hence,

• x = 13.5

Therefore,

• Length of the field = 6x = 6 × 13.5 = 81 m
• Breadth of the field = 5x = 5 × 13.5 = 67.5 m

Finding area of the field:

As we know that,

• Area of rectangle = (length × breadth) sq. units

Substituting the values,

$\sf{\longmapsto(81\times67.5)m^2}$

$\sf{\longmapsto5467.5\;m^2}$

Hence,

• Area of the field is 5467.5 m².