Question

The length and breadth of a playground are 63.5 m and 36.5 m, respectively. How long
will a man take to go round the playground thrice if he walks at the rate of 2 m/s? Also
find the cost of turfing it at 4 per square metre.​

Answer 1

Given,

The length and breadth of a playground are 63.5 m and 36.5 m respectively.

To find :

How long  will a man take to go round the playground thrice if he walks at the rate of 2 m/s.

Also find the cost of turfing it at 4 per square metre.​

Solution :

Length of playground = 63.5 m

Breadth of playground = 36.5 m

∴ Perimeter of playground = 2(63.5 + 36.5)

⇒ Perimeter of playground = 2 * 100

⇒ Perimeter of playground = 200 m

∴ Distance covered by the man = 3 * 200

∴ Distance covered by man = 600 m

· Speed of man = 2m/s

⇒ Speed = Distance/Time

⇒ 2 = 600/Time

⇒ 2 * Time = 600

⇒ Time = 600/2

⇒ Time = 300 s

∴ A man will take 300 s to go round the playground thrice.

Now,

⇒ Area of playground = Length * Breadth

⇒ Area of playground = 63.5 × 36.5

⇒ Area of playground = 2317.75 m²

· Rate of turfing = Rs. 4/m²

⇒ Cost of turfing = Area * Rate

⇒ Cost of turfing = 2317.75 * 4

⇒ Cost of turfing = Rs. 9271

∴ Cost of turfing = Rs. 9271

Answer 2

Given:-

$\bigstar$The length and breadth of a playground are 63.5 m and 36.5 m, respectively.

To Prove:-

$\bigstar$How long will a man take to go round the playground thrice if he walks at the rate of 2 meter per second.

$\bigstar$Find the cost of turfing it at 4 per square meter.

Solution:-

$\bigstar$Using formula ,

$\leadsto{ \underline{ \boxed{ \boxed{ \sf{Perimeter \: of \: playground \: = \: 2(l + b)}}}}}$

Substitute the value of length and breadth in above formula

$\leadsto{ \underline{ \boxed{ \boxed{ \sf{Perimeter \: of \: playground \: = \: 2(63.5+ 36.5)}}}}}$

$\leadsto{ \underline{ \boxed{ \boxed{ \sf{Perimeter \: of \: playground \: = \: 2 \times 100 \: = 200 \: m}}}}}$

$\bigstar$Distance covered by the man take to go round the playground thrice.

$\leadsto{\underline{\boxed{\boxed{\sf {\: 200 \times 3 = 600 \: m}}}}}$

$\bigstar$Using formula,

$\\ \leadsto{ \underline{ \boxed{ \boxed{ \sf{ \:Speed = \frac{distance}{time} }}}}}$

$\\ \leadsto{ \underline{ \boxed{ \boxed{ \sf{ \:2 = \frac{600}{time} }}}}}$

$\\ \leadsto{ \underline{ \boxed{ \boxed{ \sf{ \:Time = \frac{600}{2} = 300 \: s}}}}}$

$\bigstar$To find cost of turfing ,we have to find the area of playground

$\leadsto{ \underline{ \boxed{ \boxed{ \sf{Area\: of \: playground \: = \: l \times b}}}}}$

$\leadsto{ \underline{ \boxed{ \boxed{ \sf{Area\: of \: playground \: = \: 63.5\times 36.5}}}}}$

$\leadsto{ \underline{ \boxed{ \boxed{ \sf{Area\: of \: playground \: = 2317.75 \: {m}^{2} }}}}}$

$\bigstar$To find cost of turfing,

$\leadsto{ \underline{ \boxed{ \boxed{ \sf{Cost\: of \: turfing \: = area \: \times rate }}}}}$

$\leadsto{ \underline{ \boxed{ \boxed{ \sf{Cost\: of \: turfing \: = 2317.75 \times 4 = rs \: 9271 }}}}}$