Question

the area of rectangular path is 1728 sq.mts and ratio of length : breadth is 4;3 then breadth , length and perimeter will be

Answer 1

$\huge \textbf{ \textsf{ \color{navy}{Sol}\purple{uti}\pink{on࿐}}}$

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➠ ❝ Length and Breadth of the Rectangular park is 48mts and 36mts. ❞

➠ ❝ Perimeter of the Rectangular park is 168mts. ❞

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Step-by-step Explanation :

★ Given :

• The area of rectangular path is 1728 sq.mts
• The ratio of length : breadth is 4:3

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★ To Find :

• Value of breadth and length ?
• And also perimeter of the Rectangle ?

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★ Used Formulas :

$\large \red⇝ \: \bf Area \: _{(Rectangle)} \: = \: L×B$

$\large \red⇝ \: \bf Perimeter \: _{(Rectangle)} \: = \: 2( L + B)$

Where,

• L = Length
• B = Breadth

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★ Explanation :

The area of rectangular path is 1728 sq.mts

The ratio of length : breadth is 4:3

Let,

• Length = 4x
• Breadth = 3x

We know that,

$\bf \implies \: Area \: _{(Rectangle)} \: = \: L×B$

Now,

$\sf \implies \: 1728sq.mts\: = \: 4x×3x$

$\sf \implies \: 1728sq.mts\: = \: 12x ^{2}$

$\displaystyle\sf \implies \: \cancel\frac{1728}{12} \: = \: x ^{2}$

$\displaystyle\sf \implies \: 144 \: = \: x^{2}$

$\displaystyle\sf \implies \: 12\: = \: x$

$\displaystyle\bf \red{\implies \: \large \underline{\boxed{ \bf x \: = \: 12}}}$

Here,

• x = 12

So,

• Length = 4x = 4×12
• Breadth = 3x = 3×12

Hence,

∴ Length = 48mts

∴ Breadth = 36mts

❝ Length and Breadth of the Rectangular park is 48mts and 36mts. ❞

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Proof :

The area of rectangular path is 1728 sq.mts

The ratio of length : breadth is 4:3

Let,

• Length = 48mts
• Breadth = 36mts

We know that,

$\bf \implies \: Area \: _{(Rectangle)} \: = \: L×B \:$

Now,

$\sf \implies \: 1728sq.mts\: = \: 48mts \times 36mts$

$\bf \implies \: 1728sq.mts\: = \:1728sq.mts$

L.H.S = R.H.S

Hence proved !!

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We also know that,

$\bf \implies \: Perimeter \: _{(Rectangle)} \: = \: 2( L + B)$

We got,

• Length = 48mts
• Breadth = 36mts

So,

$\sf \implies \: Perimeter \: _{(Rectangle)} \: = \: 2( 48 + 36)$

$\sf \implies \: Perimeter \: _{(Rectangle)} \: = \: 2( 84) \:$

$\red{\implies \: \underline{ \boxed{ \bf Perimeter \: _{(Rectangle)} \: = \: \large168}}}$

Hence,

∴ Perimeter = 168mts.

❝ Perimeter of the Rectangular park is 168mts. ❞

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Proof :

In Rectangle,

• Length = 48mts
• Breadth = 36mts

We got,

Perimeter = 168mts

We know that,

$\bf \implies \: Perimeter \: _{(Rectangle)} \: = \: 2( L + B)$

Now,

$\sf \implies \: 168mts \: = \: 2(48 + 36)$

$\sf \implies \: 168mts \: = \: 2(84)$

$\bf \implies \: 168mts \: = \: 168mts$

L.H.S = R.H.S

Hence, proved !!

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