Question

$\huge\sf{Question}$
The width of a rectangular room is 3/5 of its length x metres. If its perimeter is y metres, write an equation connecting.vandy. Find the floor area of the room if its perimeter is 32 m.

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Answer 1

$\huge{ \boxed{ \color{purple}{ \sf{answer}}}}$

Let X be the Length of the Room

then ;

width =

$\frac{3}{5} \times x$

Length =

$x$

Perimeter = 2 ( L + B)

$y \: = 2(x + \frac{3x}{5} )$

Hence this is a required equation !

Now lets find AREA ;

AREA = L × B

$32 = x \times \frac{3x}{5} \\ 32 = { \frac{3x}{5} }^{2} \\ 32 \times 5 = {3x}^{2} \\ 160 = 3 {x}^{2} \\ {x}^{2} = \frac{160}{3} \\ x = \sqrt{ \frac{160}{3} }$

Answer 2

$\large{\underline{\underline{\pmb{\sf{\;Corrected\; Question\;:}}}}}$

• The width of a rectangular room is 3/5 of its length x metres. If its perimeter is y metres, write an equation connecting x and y. Find the floor area of the room if its perimeter is 32 m.

$\large{\underline{\underline{\pmb{\sf{\;Understanding\; the\; Question\;:}}}}}$

Here, we are given with the breadth/width of a rectangle is fraction of the length of rectangle, that is a variable. Also, the perimeter of rectangle is assumed as a variable. We've been asked to find an equation connecting the length and perimeter of rectangle. Also, we have been asked to calculate the area of room if the perimeter of rectangle is given.

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$\large{\underline{\underline{ \pmb{\sf{\;Solution\;:}}}}}$

⟩⟩ Given:

⋆ The width of a rectangular room is 3/5 of x.

⋆ Perimeter of rectangular room is y m.

• Let's calculate it's width by length.

$\longrightarrow\quad\sf{Width=\dfrac{3}{5}\; of\; x}$

Now, converting fraction into decimal.

$\longrightarrow\quad\sf{Width=0.6\: x}$

Now, let's calculate the equation connecting x and y. We know,

$\longrightarrow\quad\sf{Perimeter=2(l+b)}$

Substituting all the values we know:

$\longrightarrow\quad\sf{y=2(x+0.6x)}$

Performing addition and multiplication, we get:

$\longrightarrow\quad\underline{\boxed{\sf{y=3.2\: x}}}$

$\qquad\leadsto$ Therefore, the equation connecting x and y is y = 3.2 x.

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Now, let's assume the perimeter of rectangular room as 32 m. Then,

$\longrightarrow\quad\sf{Perimeter\; as\; per\; equation=Perimeter}$

Equating the values:

$\longrightarrow\quad\sf{3.2x=32}$

$\longrightarrow\quad\sf{x=\dfrac{32}{3.2}}$

Performing division.

$\longrightarrow\quad\sf{x=10\: m}$

Therefore:

• Length = x = 10 m
• Breadth = 0.6 x = 6 m

Now, we know:

$\longrightarrow\quad\sf{Area=length\times breadth}$

Substituting all the values:

$\longrightarrow\quad\sf{Area=10\times 6}$

Performing multiplication:

$\longrightarrow\quad\underline{\boxed{\sf{Area=60\; {m}^{2}}}}$

❝Therefore, the area of rectangular room is 60 m².❞