Question

(1) . A dining hall is 30m long and 28m broad. The hall needs to be carpeted

having a margin of 1m all around. Find the length and breadth of the carpet required

and the cost of carpeting at the rate of 120 per m2

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Answer 1

Given Question :-

• A dining hall is 30m long and 28m broad. The hall needs to be carpeted having a margin of 1 m all around. Find the length and breadth of the carpet required and the cost of carpeting at the rate of Rs 120 per square meter.

Answer

Given :-

• A dining hall is 30m long and 28m broad.

• The hall needs to be carpeted having a margin of 1m all around.

• The cost of carpeting is Rs 120 per square meter.

To Find :-

• The length and breadth of the carpet required.

• Cost of carpeting the area.

CALCULATION :-

Given

• Dimensions of dining hall

• Length of dining hall = 30 m

• Breadth of dining hall = 28 m

Now,

$\large \underline{\tt \:{ According \: to \: statement }}$

• The dining hall is to be carpeting by leaving a margn of 1 m all around.

So,

Dimensions of area to be carpet is

• Length of carpeting area = 30 - 1 - 1 = 28 m

• Breadth of carpeting area = 28 - 1 - 1 = 26 m

So,

• Area covered by carpet is evaluated as

$\rm :\longmapsto\:Area_{(carpet)} = length \times breadth$

$\rm :\longmapsto\:Area_{(carpet)} = 28 \times 26$

$\rm :\longmapsto\:Area_{(carpet)} = 728 \: {m}^{2}$

Now,

$\rm :\longmapsto\:Cost \: of \: carpeting \: 1 \: {m}^{2} = Rs \: 120$

$\rm :\longmapsto\:Cost \: of \: carpeting \: 728 \: {m}^{2} = Rs \: 120 \times 728$

$\rm :\longmapsto\:Cost \: of \: carpeting \: 728 \: {m}^{2} = Rs \: 87360$

$\begin{gathered}\begin{gathered}\boxed{\begin {array}{cc}\\ \dag\quad \Large\underline{\bf Formulas\:of\:Areas:-}\\ \\ \star\sf Square=(side)^2\\ \\ \star\sf Rectangle=Length\times Breadth \\\\ \star\sf Triangle(right)=\dfrac{1}{2}\times Breadth\times Height \\\\ \star \sf Scalene \: \triangle=\sqrt {s (s-a)(s-b)(s-c)}\\ \\ \star \sf Rhombus =\dfrac {1}{2}\times d_1\times d_2 \\\\ \star\sf Rhombus =\:\dfrac {1}{2}d\sqrt {4a^2-d^2}\\ \\ \star\sf Parallelogram =Breadth\times Height\\\\ \star\sf Trapezium =\dfrac {1}{2}(a+b)\times Height \\ \\ \star\sf Equilateral\:Triangle=\dfrac {\sqrt{3}}{4}(side)^2\end {array}}\end{gathered}\end{gathered}$