Question

A rectangular playing ground is 25m long and 15m broad. A path of 3metres width is all around inside it along the border. find the area of path

Answer 1

Answer:

{\large{\bold{\sf{\underline{Understanding \; the \; question}}}}}

Understandingthequestion

➨ This question says that the rectangular playground has length as 25 metres and 15 metres as breadth. A path of 3 metres width ( breadth ) is all around inside it along the border. We have to find the area of that path.

{\large{\bold{\sf{\underline{Given \; that}}}}}

Giventhat

➨ Length of rectangular playground = 25 metres.

➨ Breadth of rectangular playground = 15 metres.

➨ Path of 3 metres in breadth is all around inside it along the border.

{\large{\bold{\sf{\underline{To \; find}}}}}

Tofind

➨ Area of path.

{\large{\bold{\sf{\underline{Solution}}}}}

Solution

➨ Area of path = 276 m²

{\large{\bold{\sf{\underline{Using \; concepts}}}}}

Usingconcepts

➨ Area of rectangle formula.

{\large{\bold{\sf{\underline{Using \; formulas}}}}}

Usingformulas

➨ Area of rectangle = Length × Breadth

{\large{\bold{\sf{\underline{We \; also \; write \; these \; as}}}}}

Wealsowritetheseas

➨ Length as L

➨ Breadth as B

➨ Area as A

{\large{\bold{\sf{\underline{Full \; Solution}}}}}

FullSolution

~ Let us find area of that rectangular playground firstly'

➸ Area of rectangular playground = Length × Breadth

➸ Area of rectangular playground = (25 × 15) metres

➸ Area of rectangular playground = 375 m²

~ Now let's find area of that playground including border and inside area

➸ Length = ( 25 + 3 + 3 ) m = 31 m

➸ Breadth = ( 15 + 3 + 3 ) m = 21 m

➸ Area = Length × Breadth

➸ Area of = ( 31 × 21 ) metres

➸ Area = 651 m²

~ Now at last let us find area of path

➸ Area of path = Area of playground including border and inside area - rectangular playground area

➸ Area of path = ( 651 - 375 ) m²

➸ Area of path = 276 m²

( Diagram of this question is in attachment )

{\large{\bold{\sf{\underline{Knowledge}}}}}

Knowledge

}

Perimeter of rectangle formula = 2(length + breadth)

Area of rectangle formula = Length × Breadth.

Answer 2

${\large{\bold{\sf{\underline{Understanding \: \: The \: \: Question}}}}}$

➨ This question says that the rectangular playground has length as 25 metres and 15 metres as breadth. A path of 3 metres width ( breadth ) is all around inside it along the border. We have to find the area of that path.

${\large{\bold{\sf{\underline{Given \; that}}}}}$

➨ Length of rectangular playground = 25 metres.

➨ Breadth of rectangular playground = 15 metres.

➨ Path of 3 metres in breadth is all around inside it along the border.

${\large{\bold{\sf{\underline{To \; find}}}}}$

➨ Area of path.

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

➨ Area of path = 276 m²

${\large{\bold{\sf{\underline{Using \; concepts}}}}}$

➨ Area of rectangle formula.

${\large{\bold{\sf{\underline{Using \; formulas}}}}}$

➨ Area of rectangle = Length × Breadth

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

➨ Length as L

➨ Breadth as B

➨ Area as A

${\large{\bold{\sf{\underline{Full \; Solution}}}}}$

${ \color{blue}{ ~Let \: \: us \: \: find \: \: area \: \: of \: \: that \: \: rectangular \: \: playground \: \: firstly'}}$

➸ Area of rectangular playground = Length × Breadth

➸ Area of rectangular playground = (25 × 15) metres

➸ Area of rectangular playground = 375 m²

${ \color{green}{~ Now \: \: let's \: \: find \: \: area \: \: of \: \: that \: \: playground \: \: including \: \: border \: \: and \: inside \: \: area}}$

➸ Length = ( 25 + 3 + 3 ) m = 31 m

➸ Breadth = ( 15 + 3 + 3 ) m = 21 m

➸ Area = Length × Breadth

➸ Area of = ( 31 × 21 ) metres

➸ Area = 651 m²

${ \color{red}{~ Now \: at \: last \: let \: us \: find \: area \: of \: path}}$

➸ Area of path = Area of playground including border and inside area - rectangular playground area

➸ Area of path = ( 651 - 375 ) m²

➸ Area of path = 276 m²

( Diagram of this question is in attachment )

${\large{\bold{\sf{\underline{Knowledge}}}}}$

Rectangle diagram -

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Rectangle with Diagonal -

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\put(0.03,2.74){\framebox(0.25,0.25)}\put(4.74,0.01){\framebox(0.25,0.25)}\put(2,-0.7){\sf\large x cm}\put(-0.5,-0.4){\bf A}\put(-0.5,3.2){\bf D}\put(5.3,-0.4){\bf B}\put(5.3,3.2){\bf C}\qbezier(0,0)(0,0)(5,3)\put(1.65,1.8){\sf\large y cm}\end{picture}</p><p>$

Perimeter of rectangle formula = 2(length + breadth)

Area of rectangle formula = Length × Breadth.

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