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

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

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

Let the breadth be x

.and the length be 3x

Now :--

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

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

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

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

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

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

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

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

$\boxed{\bold{The\: length\: of \:carpet\: is \:4.8cm}}$

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