Math, asked by satishthandya, 5 months ago

10. The perimeter of a rectangle is equal to the perimeter of a square. If the length and
breadth of rectangle is 20 m and 10 m, respectively. Find the area of the squar.
(1) 300 sq m (2) 225 sqm
(3) 250 sqm
(4) 325 sqm​

Answers

Answered by DynamicCrystal
12

AnsweR :

 \sf option \: (2) \:  {225m}^{2}

ExplanatioN :

 \sf \: perimeter \: of \: rectangle = perimeter \: of \: square

 \sf  \bold {perimeter \: of \: rectangle = 2(l + b)}

 \sf \bold{ perimeter \: of \: square \:  =  \: 4 \times a}

  = \sf 2(l + b) = 4 \times a

 \sf \: l = 20m \\  \sf \: b = 10m

  \sf= 2(20 + 10) = 4 \times a \\  \\  \sf = 40 + 20 = 4a \\  \\  \sf = 60 = 4a \\  \\  \sf = a =  \frac{ \cancel{60}}{ \cancel4}  = 15m

 \sf \: side \: of \: the \: square = 15m

 \sf \bold {area \: of \: the \: square \:  = side \times side}

 \sf = side  \times side \\  \\  \sf = 15 \times 15 \\  \\  \sf = {225m}^{2}

Answered by Cordelia
10

\:\:\:\: \Large \underline {\sf{Given\::}}

➟ Perimeter of rectangle is equal to the perimeter of square

➟ Length and breadth of rectangle is 20 cm and 10 cm respectively

\:\:\:\: \Large \underline {\sf{To\:Find\::}}

➟ Area of square

\:\:\:\: \Large \underline {\sf{Solution\::}}

Let us find perimeter of rectangle :

\underline{\boxed{\sf{\pink{Formula\:used\:=\: 2( l\:+\:b) }}}} \\ \\

➟ 2 ( l + b )

➟ 2 ( 20 + 30 )

➟ 2 ( 30 )

➟ 60 m

\:\:\:\: \therefore \large \underline {\sf{Perimeter\:of\:Square\:=\:60\:m}} \\ \\

Let us find side of square :

\underline{\boxed{\sf{\pink{Formula\:used\:=\: \dfrac{Perimeter}{4} }}}} \\ \\

\sf \cancel \dfrac{60}{4}

\sf 15\:m \\ \\

\:\:\:\: \large \underline {\sf{Side\:of\:Square\:=\:15\:m}} \\ \\

Let us find area of square :

\underline{\boxed{\sf{\pink{Formula\:used\:=\: Side \times Side \:=\:{Side}^{2}}}}} \\ \\

\sf 15 \times 15

\sf 225\:{m}^{2} \\ \\

\:\:\:\:\:\: \Large {\underline{\underline{\sf{Area\:of\:Square\:=\:225\:{m}^{2}}}}} \\ \\ \\

Option (2) is correct i.e. 225

Final ans is 225

And we are done !

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Sen0rita: kamaal kardiya xD ❤️
Cordelia: Shukriya xD ❤️
Sen0rita: xD ❤️
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