Question

8. Lata jogs seven rounds of a square park with side
95m. Next day, she takes five rounds of a rectangula
walking track measuring 200m x 100m. Which
option (i.e., square park or rectangular track) will
provide a longer walk and by how much?

Answer 1

Answer :-

$\\\;\underbrace{\underline{\sf{Understanding\;the\;Question\;:-}}}$

Here the concept of Perimeter of Square and Perimeter of Rectangle has been used. In order to compare that which track will provide longer walk, we need to find the length that is given to be walked by each track. Firstly we need to find Perimeter of each track and then multiply it with the number of rounds taken. Then we need to compare it.

Let's do it !!

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★ Formula Used :-

$\\\;\boxed{\sf{Perimeter\;of\;Square\;=\;\bf{4\;\times\;Side}}}$

$\\\;\boxed{\sf{Perimeter\;of\;Rectangle\;=\;\bf{2(Length\;+\;Breadth)}}}$

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★ Solution :-

Given,

» Side of Square = 95 m

» Length of the Rectangular Park = 200 m

» Breadth of the Rectangle Park = 100 m

» No. of rounds taken around Square Park = 7

» No. of rounds taken around Rectangular Park = 5

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~ For the Distance covered in Square Park ::

First we shall find the distance covered in single round. This is given as -

$\\\;\;\;\sf{:\rightarrow\;\;Perimeter\;of\;Square\;=\;\bf{4\;\times\;Side}}$

$\\\;\;\;\sf{:\rightarrow\;\;Perimeter\;of\;Square\;=\;\bf{4\;\times\;95}}$

$\\\;\;\;\sf{:\rightarrow\;\;Perimeter\;of\;Square\;=\;\bf{4\;\times\;95}}$

$\\\;\;\;\bf{:\rightarrow\;\;Perimeter\;of\;Square\;=\;\bf{380\;\;m}}$

Now distance covered by 7 rounds -

$\\\;\;\;\sf{:\Longrightarrow\;\;Total\;distance\;covered\;=\;\bf{No.\;of\;Rounds\;\times\;Perimeter}}$

$\\\;\;\;\sf{:\Longrightarrow\;\;Total\;distance\;covered\;=\;\bf{7\;\times\;380}}$

$\\\;\;\;\bf{:\Longrightarrow\;\;Total\;distance\;covered\;=\;\bf{2660\;\;m}}$

$\\\;\underline{\boxed{\tt{Total\;\;distance\;\;covered_{(Square\;Park)}\;=\;\bf{2660\;\;m}}}}$

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~ For Distance covered in Rectangular Park ::

Let's first calculate distance covered in 1 round -

$\\\;\;\;\sf{:\rightarrow\;\;Perimeter\;of\;Rectangle\;=\;\bf{2(Length\;+\;Breadth)}}$

$\\\;\;\;\sf{:\rightarrow\;\;Perimeter\;of\;Rectangle\;=\;\bf{2(200\;+\;100)}}$

$\\\;\;\;\sf{:\rightarrow\;\;Perimeter\;of\;Rectangle\;=\;\bf{2(300)}}$

$\\\;\;\;\bf{:\rightarrow\;\;Perimeter\;of\;Rectangle\;=\;\bf{600\;\;m}}$

Now distance covered in 5 rounds -

$\\\;\;\;\sf{:\Longrightarrow\;\;Total\;distance\;covered\;=\;\bf{No.\;of\;Rounds\;\times\;Perimeter}}$

$\\\;\;\;\sf{:\Longrightarrow\;\;Total\;distance\;covered\;=\;\bf{5\;\times\;600}}$

$\\\;\;\;\bf{:\Longrightarrow\;\;Total\;distance\;covered\;=\;\bf{3000\;\;m}}$

$\\\;\underline{\boxed{\tt{Total\;\;distance\;\;covered_{(Rectangle\;Park)}\;=\;\bf{3000\;\;m}}}}$

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~ For Comparison between two tracks :-

Clearly, 3000 m > 2660 m

Thus,

• Rectangular Track > Squared Track

This difference can be calculated as ::

✒ 3000 - 2660

✒ 340 m

✏ Hence, Rectangular track is longer than square track by 340 m

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★ More to know :-

$\\\;\sf{\leadsto\;\;Area\;of\;Square\;=\;(Side)^{2}}$

$\\\;\sf{\leadsto\;\;Area\;of\;Rectangle\;=\;Length\;\times\;Breadth}$

$\\\;\sf{\leadsto\;\;Area\;of\;Circle\;=\; \pi r^{2}}$

$\\\;\sf{\leadsto\;\;Perimeter\;of\;Circle\;=\;2 \pi r}$

$\\\;\sf{\leadsto\;\;Area\;of\;Triangle\;=\;\dfrac{1}{2}\;\times\;Base\;\times\;Height}$

$\\\;\sf{\leadsto\;\;Area\;of\;Parallelogram\;=\;Base\;\times\;Height}$

Answer 2

${\bold{\sf{\underline{Solution}}}}$

✠ Rectangular park provided longer walk except of square park. And their difference is of 340 metres !

${\bold{\sf{\underline{Let's \: understand \: the \: question}}}}$

✠ This question says that Lata jogs seven rounds of a square park with side 95m. Next day, she takes five rounds of a rectangular park ; walking track measuring 200m x 100m. Which option (i.e., square park or rectangular track) will provide a longer walk and by how much?

✠ In short this question says that Lata jogs in a square park and it's of side 95 metres and she take 7 rounds. Next day, she jogs in rectangular park and it's dimensions are 200 metres × 100 metres. Means it's length and breadth are 200 m and 100 m respectively. Afterwards this question ask us to find square park or rectangular track) will provide a longer walk and by how much ?

${\bold{\sf{\underline{Given \: that}}}}$

✠ Number of round taken in square park = 7

✠ Side of square park = 95 m

✠ Length of rectangular park = 200 m

✠ Breadth of rectangular park = 100 m

✠ Number of round taken in rectangular park = 5

${\bold{\sf{\underline{To \: find}}}}$

✠ Which option (i.e., square park or rectangular track) will provide a longer walk and by how much ?

${\bold{\sf{\underline{Using \: concepts \: and \: formulas}}}}$

✠ Perimeter of rectangle = 2(length + breadth)

✠ Perimeter of square = 4 × sides

✠ Total distance = No. of total rounds × Perimeter { ATQ }

${\bold{\sf{\underline{We \: also \: write \: these \: as}}}}$

✠ Length as l

✠ Breadth as b

✠ Perimeter as P

${\bold{\sf{\underline{Full \: solution}}}}$

✠ Let's find the distance rounded in square park. As we already know that there are 7 rounds taken there. But firstly we have to find the distance taken in a round then of 7 rounds.

1 round

↦ P of square = 4 × S

↦ P of square = 4 × 95

↦ P of square = 380 m

7 rounds

↦ Total dstance = No. of total rounds × P ( 1 round finded )

↦ Total dstance = 7 × 380

↦ Total distance = 2660 m

✠ Let's find the distance rounded in rectangular park now. As we already know that there are 5 rounds taken there. But firstly we have to find the distance taken in a round then of 5 rounds.

1 round

↦ P of rectangle = 2(l+b)

↦ P of rectangle = 2(200+100)

↦ P of rectangle = 2(300)

↦ P of rectangle = 600 m

5 rounds

↦ Total distance = No. of total rounds × P ( 1 round finded )

↦ Total distance = 5 × 600

↦ Total distance = 3000 m

✠ Now let's do the comparison means let's compare the square track and rectangular track. As we already see that Rectangular park = 3000 metres and square park = 2660 metres. That's why it's clearly that

↦ Square park < Rectangular park

↦ 2660 m < 3000 m

✠ Now let's calculate the difference

↦ (3000 - 2660) m

↦ 340 m