Question

The length and breadth of a rectangular park are 120 m and 70 m. A jogging track 2 m wide runs along
the sides on the inside of the boundary of the park. A man runs 3 times on the jogging track.
How much distance does he cover?​

Answer 1

Given:

• The length and breadth of a rectangular park are 120 m and 70 m.

• A jogging track 2 m wide runs alongthe sides on the inside of the boundary of the park.

• A man runs 3 times on the jogging track.

To Find:

• How much distance does he cover?

Solution:

●Here,

➱ It is said that there is a rectangle surrounded by a path.

an athlete runs 3 times around it, and that we have to find the distance covered by him

● So,

➱ We have to firstly find the dimensions of the path and then find its perimeter which would give us the distance covered by the athlete in one round.

Now,

• ⇢ Length of the park = 120meter
• ⇢ Breadth of the park = 70m

As we know that,

• The path 2m is surrounded inside the park

So,

• ↝ Length of the path = 120 - (2 + 2) = 116m
• ↝ Breadth of the path = 70 - (2 + 2) = 66m

➱ Now let's find the perimeter of the path

➼ Formula :-

$\star{ \pink{ \boxed{ \frak{perimeter_{(rectangle)} = 2(l + b)}}}}$

Where,

• L Stands for length
• B Stands for breadth

Here,

• Length = 116m
• Breath = 66m

Substituting the values we get,

${ : \implies} \rm \: perimeter _{(path)} = 2(116 + 66)m \\ \\ \\ { : \implies} \rm \: perimeter _{(path)} = \: 2(182)m \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \rm \: perimeter _{(path)} =364m \bigstar \: \: \: \: \: \: \: \: \: \:$

• Hence, The distance covered by the athlete in 1 round is 364m

Now,

• We have to find the distance covered in 3 rounds

So,

➠ Distance covered in 3 rounds = 364 × 3 m

➠ Distance covered in 3 rounds = 1092m

➠ Distance covered in 3 rounds= 1.092km

Hence:

• The distance covered by the athlete is 1092m/1.002km

$\large{ \underline{ \pmb{ \frak{Additional \: information ...}}}}$

$\begin{gathered}\boxed{\begin {array}{cc}\\ \dag\quad \Large\underline{\bf Formulas\:of\:Areas:-}\\ \\ \star\sf Square=(side)^2\\ \\ \star\sf Rectangle=Length\times Breadth \\\\ \star\sf Triangle=\dfrac{1}{2}\times Breadth\times Height \\\\ \star \sf Scalene\triangle=\sqrt {s (s-a)(s-b)(s-c)}\\ \\ \star \sf Rhombus =\dfrac {1}{2}\times d_1\times d_2 \\\\ \star\sf Rhombus =\:\dfrac {1}{2}p\sqrt {4a^2-p^2}\\ \\ \star\sf Parallelogram =Breadth\times Height\\\\ \star\sf Trapezium =\dfrac {1}{2}(a+b)\times Height \\ \\ \star\sf Equilateral\:Triangle=\dfrac {\sqrt{3}}{4}(side)^2\end {array}}\end{gathered}$

Answer 2

Given:

• The length and breadth of a rectangular park are 120 m and 70 m.

• A jogging track 2 m wide runs along
• the sides on the inside of the boundary of the park.

To Find:

• The distance covered by a man who runs 3 times on the jogging track!

Solution:

We know that,

• ➱ Length of the park = 120m
• ➱ Breadth of the park = 70m

Now,

➼ A jogging track 2 m wide runs along

the sides on the inside of the boundary of the park.

So,

• Length of the trak = 116m
• Breath of the trak = 66m

The distance covered by the man

• Will be three times the boundary of the trak

Perimeter of a rectangle : -

• 2 ( Length + Breadth)

Distance covered : -

➱ 2 ( Length + Breadth) × 3

➱ 2 ( 116 + 66 ) × 3

➱2 ( 182 ) × 3

➱ 364 × 3

➱ 1092m

Hence:

• The distance covered by the athlete is 1092m

Hope this helps!!