Question

the length and breadth of a Park are in the ratio 2:1 and its perimeter is 240 m . A path 2 m wide runs inside it, along its boundary. find the cost of paving the path at $ 3 per square metre.






solve the problem please.

Answer 1

$\textbf {Hey there, here is the solution.}$

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Ratio of Length : Breadth = 2 : 1 (Given)

.

STEP 1: Find the length and Breadth

Let x be the constant ratio

The perimeter is 240 m:

2(2x + 1x) = 240

2(3x) = 240

6x = 240

x = 40 cm

.

Breadth = x = 40 cm

Length = 2x = 2(40) = 80 cm

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STEP 2: Find the area of the park:

Area of the park = 40 x 80 = 3200 m²

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STEP 3: Find the area of the inner park:

Length = 80 - 2 - 2 = 76 m

Breadth = 40 - 2 - 2 = 36 m

Area = 76 x 36 = 2736 m²

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STEP 4: Find the area of the path:

3200 - 2736 = 464 m²

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STEP 5: Find the cost of paving:

1 m² = $3

464 m² = 3 x 464 = $1392

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Answer: The cost of paving the path is $1392

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$\textbf {Cheers}$

Answer 2

Let us name the (rectangular) park $\red{ABCD}$

It's ratio of length and breadth = 2 : 1 $\bf{ (Given) }$

It's perimeter = 240 m $\bf{ (Given) }$

Let,
length be $\orange{2x }$
breadth be $\pink{1x }$

We know that,
Perimeter of rectangle = 2( $\orange{2x }$ + $\pink{1x }$ ) [ in which $\orange{'l' }$ is $\orange{'length' }$ and $\pink{'b' }$ is $\pink{'breadth' }$ ]

so,
➡ 240 = 2( $\orange{2x }$ + $\pink{1x }$ )

➡ 240 = $\orange{4x }$ + $\pink{2x }$

➡ 240 = 6x

➡ 240÷6 = x

➡ 40 = x

Now,
length = $\orange{2x }$ = $\orange{2*40 = 80m }$

breadth = $\pink{1x }$ = $\pink{1*40 = 40m }$

Area of park = $\orange{length }$ ×$\pink{breadth}$

= $\orange{80 }$ × $\pink{40 }$ = $\bf{3200 }$m²

$\bf{According\: \: to\: \: the\: \: question}$,
A path 2m wide runs inside the $\red{ABCD}$ along its boundary.

Let the inner park be named as $\blue{PQRS}$

it's length = 80 -2 -2 = 76 m
it's breadth = 40 -2 -2 = 36 m

it's area = 76 × 36 = $\bf{2736}$ m²

Now,
area of the path = $\red{area \: \: of \: \:ABCD}$ - $\blue{area \: \: of \: \:PQRS}$

area of path = $\red{3200}$ - $\blue{2736}$ = $\purple{464}$ m²

If the cost of paving the path per m² = $3
So,
cost of paving 464 m² = 464 × 3 = $ 1392

Hence,
Cost of paving the path = $ $\bf{1392}$.