Question

the perimeter of rectangular room whose length is three times its breadht is 64 m . find the lenght of carpet ,40 cm wide required for the room.​

Answer 1

$\huge\mathbb{\underline{\underline{SOLUTION:-}}}$

$\bold{Given}\begin{cases}\sf{Perimeter\:of\: rectangular\:room =64m}\end{cases}$

• Let the breadth be x
• .and the length be 3x

Now '-

$\bf{\underline{\underline{According\:To\: Question:-}}}$

$\tt perimeter\:of\: rectangle=2(L+B)$

$\begin{cases}\sf{Length=3x}\\ \sf{Breadth=x}\\ \sf{perimeter=64m}\end{cases}$

$\tt perimeter=2(L+B)\\ \\ \tt\leadsto 64=2(x+3x)\\ \\ \tt\leadsto 64=2\times 4x \\ \\ \tt\leadsto \frac{\cancel{64}}{\cancel2}=4x\\ \\ \tt\leadsto 32=4x\\ \\ \tt\leadsto \frac{\cancel{32}}{\cancel{4}}=x\\ \\ \sf\implies x=8cm$

$\sf Breadth=8cm \\ \sf length =8\times 24cm$

• $\sf Area\:of\: rectangle=L×B\\ \\ \sf Area=24\times 8\\ \\ \sf\implies 192cm{}^{2}$

$\bold{Given}\begin{cases}\sf{Width\:of\:carpet=40cm}\\ \sf{Area\:of\:room=192cm{}^{2}}\end{cases}$

$\sf Area \:of\:room=Area\:of\:carpet\\ \\ \sf\leadsto 192=40×x\\ \\ \sf Let\:length\:be\:x\\ \\ \bf Now:-\\ \\ \tt\leadsto \frac{\cancel{192}}{\cancel{40}}=x\\ \\ \tt\implies x=4.8$

The length of carpet is 4.8cm

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Answer 2

$\underline \mathbb{SOLUTION}$

$\underline \mathbb{GIVEN}$

PERIMETER OF RECTANGULAR ROOM = 64 m.

$\underline \mathbb{LET}$

$breadth = x$

$length = 3x$

$\underline \mathbb{NOW}$

ATQ,

$perimeter \: of \:rectangle = 2(l + b)$

$lenght = 3x$

$breadth = x$

$perimeter = 64m$

$perimeter = 2(l + b)$

$= > 64 = 2(x + 3x)$

$= > 64 = 2 \times 4x$

$= > \frac{64}{2} = 4x$

$= > 32 = 4x$

$= > \frac{32}{4} = x$

$= > x = 8cm$

•Breadth= 8 cm

•Length = 8×24 cm

$area = l \times b$

$area = 24 \times 8$

$= > 192 {cm}^{2}$

$\underline \mathbb{GIVEN}$

$width \: of \: carpet = 40cm$

$area \: of \: room \: = 192 {cm}^{2}$

•Area of room = Area of carpet

$= > 192 = 40 \times x$

$\underline \mathbb{LET}$

$length \: be \: x$

NOW,

$= > \frac{192}{40} = x$

$= > x = 4.8$

HENCE,

THE LENGTH OF CARPET IS 4.8 cm.

_____________________________________

#BAL

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