Question

A room is 13 m long 9 m wide find the cost of carpeting it at 60 rs per metre if the carpet is 75 cm wide

Answer 1

Step-by-step explanation:

Given :

Dimensions of room = 13m × 9m

Side of carpet = 75 cm

Rate of carpeting = Rs. 60 per m

To find :

The Cost of carpeting

Solution :

★ Area of the room -

⇒ Area = Length × Breadth

⇒ 13 × 9

⇒ 117 m²

$\rule{300}{1.5}$

★ Area of the carpet -

⇒ Area = Side × Side

⇒ 0.75 m × 0.75 m

⇒ 0.5625 m²

$\rule{300}{1.5}$

★ Area covered by the carpet -

⇒ Area of room / Area of carpet

⇒ 117/0.5625

⇒ 1170000/5625

⇒ 208 m²

$\rule{300}{1.5}$

★ Cost of carpeting -

⇒ 208 × 60

⇒ 12,480

Cost = Rs. 12,480

Therefore, the cost of carpeting is Rs. 12,480.

Answer 2

Answer:

⋆ DIAGRAM :

$\setlength{\unitlength}{1.5cm}\begin{picture}(8,2)\thicklines\put(7.3,2){\sf{\large{9 m}}}\put(9.2,0.7){\sf{\large{13 m}}}\put(8,1){\line(1,0){3}}\put(8,1){\line(0,2){2}}\put(11,1){\line(0,3){2}}\put(8,3){\line(3,0){3}}\end{picture}$

$\rule{90}{2}$

$\underline{\bigstar\:\:\textsf{Area of Room :}}$

$:\implies\tt Area=Length \times Breadth\\\\\\:\implies\tt Area=13m \times 9m\\\\\\:\implies\tt Area=(13 \times 100)cm \times (9 \times 100)cm\\\\\\:\implies\tt Area=1300cm \times 900cm\\\\\\:\implies\tt Area=1170000\:cm^2$

$\rule{160}{1}$

$\underline{\bigstar\:\:\textsf{Length of Carpet Required :}}$

$:\implies\tt Area_{Room}=(Length \times Width)_{carpet}\\\\\\:\implies\tt 1170000\:cm^2=Length \times 75\:cm\\\\\\:\implies\tt \dfrac{1170000\:cm^2}{75\:cm}=Length\\\\\\:\implies\tt Length=15600\:cm\\\\\\:\implies\tt Length=156\:m$

$\rule{200}{2}$

$\underline{\bigstar\:\:\textsf{Cost of Carpeting the Room :}}$

$\dashrightarrow\tt\:\:Cost=Length_{carpet} \times Rate\\\\\\\dashrightarrow\tt\:\:Cost=156\:m \times Rs.\:60\:m^{-1}\\\\\\\dashrightarrow\tt\:\:Cost=156 \times Rs. 60\\\\\\\dashrightarrow\:\:\underline{\boxed{\textsf{\textbf{Cost = Rs. 9,360}}}}$

⠀

$\therefore\:\underline{\textsf{Cost of carpeting of room is \textbf{Rs. 9,360}}}.$