Question

UCNISTUUS OI UIC DUX.
the length and breadth of the room.
14. The length and breadth of a hall are in the ratio 4:3 and its height is 5.5 metres. The cost of
decorating its walls (including doors and windows) at 6.60 per square metre is 5082. Find​

Answer 1

$\huge\mathcal\colorbox{red}{{\color{white}{[] answer[] }}}[]$

let length be 4x cm and breadth be 3x cm

height=550cm

rate of decorating wall= Rs 6.60/m²

total cost of decorating wall= Rs 5082

total cost= area to be decorated × rate

5082=2(lh+bh)×6.6

5082×10=2×550×(4x+3x)×66/100

231×100=2×55×7x×3

21×100=2×5×21x

10=x

∴length =4×10=40m

breadth=3×10=30m

Answer 2

Given Question :-

• The length and breadth of a hall are in the ratio 4:3 and its height is 5.5 metres. The cost of decorating its walls (including doors and windows) at 6.60 per square metre is 5082. Find the length and breadth of the room.

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$\huge \orange{AηsωeR} ✍$

${ \boxed {\bf{Given}}}$

• The length and breadth of a hall are in the ratio 4:3.
• Its height is 5.5 metres.
• The cost of decorating its walls (including doors and windows ) at ₹ 6.60 per square metre is ₹ 5082.

$\begin{gathered}\Large{\bold{\purple{\underline{To\:FiNd\::}}}} \end{gathered}$

$\bf \:➣ Length \: and \: Breadth \: of \: hall.$

$\begin{gathered}\Large{\underline{\bf{\color{purple}CaLcUlAtIoN,}}} \end{gathered}$

$\begin{gathered}\bf\red{Let,} \end{gathered}$

$\begin{gathered}\longmapsto\:\:\bf{Length\:(l) \:is \:4x\:m}. \\ \end{gathered}$

$\begin{gathered}\longmapsto\:\:\bf{Breadth\:(b) \:is \:3x\:m}. \\ \end{gathered}$

$\begin{gathered}\longmapsto\:\:\bf{Height\:(h) \:is \:5.5\:m}. \\ \end{gathered}$

$\begin{gathered}\red\checkmark\:\:\bf{Area\:of\:4\:walls\:=2(l + b) \times h} \\ \end{gathered}$

$\bf \:  ⟼ Area\:of\:4\:walls\:=2(4x + 3x) \times 5.5$

$\bf \:  ⟼ Area\:of\:4\:walls\:=11 \times 7x$

$\bf \:  ⟼ Area\:of\:4\:walls\:=77x \: ⟼ (1)$

$\bf\red{According\:to\:the\:question,}$

☆ The cost of decorating its walls (including doors and windows) at 6.60 per square metre is 5082.

$\bf \:  ⟼ Area\:of\:4\:walls\:=\dfrac{5082}{6.60} = 770 \: {m}^{2}$

☆ On equating above and equation (1), we get

$\bf \:  ⟼ 77x = 770$

$\bf \:  ⟼ x = \dfrac{770}{77}$

$\begin{gathered}:\implies\:\:\bf\green{x\:=\:10} \end{gathered}$

$\begin{gathered}\Large\bf\green{Hence,} \end{gathered}$

$\bf \:➣ Breadth = 3 \times 10  = 30 \: m.$

$\begin{gathered}\bf\red{And,} \end{gathered}$

$\begin{gathered}\longmapsto\:\:\bf{Length\:(l) \:= \:4\times{10}} = 40 \: m \end{gathered}$

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${ \boxed {\bf{More  \: information}}}$

Perimeter of rectangle = 2(length× breadth)

Diagonal of rectangle = √(length²+breadth²)

Area of square = side²

Perimeter of square = 4× side

Volume of cylinder = πr²h

T.S.A of cylinder = 2πrh + 2πr²

Volume of cone = ⅓ πr²h

C.S.A of cone = πrl

T.S.A of cone = πrl + πr²

Volume of cuboid = l × b × h

C.S.A of cuboid = 2(l + b)h

T.S.A of cuboid = 2(lb + bh + lh)

C.S.A of cube = 4a²

T.S.A of cube = 6a²

Volume of cube = a³

Volume of sphere = 4/3πr³

Surface area of sphere = 4πr²

Volume of hemisphere = ⅔ πr³

C.S.A of hemisphere = 2πr²

T.S.A of hemisphere = 3πr²

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