Question

a rectangular hall is 22 metre long and 15.5 m board a carpet is laid inside the hole leaving all around margin of 75 cm from the wall find the area of the carpet and the area of the strip left and covered if the visit of the carpet is 82 cm find its cost @ rupees 124 per metre​

Answer 1

Solution :

Let ABCD be a rectangular hall and EFGH be left margin.

$\star \tt \: Length \: of \: hall = 22 \: m$

$\star \tt \: Breadth \: of \: hall \: = 15.5 \: m$

___________________

$\star \rm \: Area \: of \: hall = length \times breadth$

$\hookrightarrow \sf \: 22 \times 15.5m$

$\hookrightarrow \sf \: 341 {m}^{2}$

______________

$\star \tt \: Margin = 75cm = 0.75 \: m$

______________

$\star \rm \: Area \: of \: carpet = \\ \sf \: (length - 2 \times margin)(breadth - 2 \times margin)$

$\hookrightarrow \sf \: (22 - 2 \times 0.75) \: (15.5 - 2 \times 0.75)$

$\hookrightarrow \sf \: \: (22 - 1.5) \: (15.5 - 1.5)$

$\hookrightarrow \sf \: \: 20.5 \times 14$

$\hookrightarrow \large \boxed{ \sf \: 287 {m}^{2} }$

_______________

$\star \tt \: Left \: area = \\ \tt Area \: of \: rectangle \: - \: Area \: of \: carpet$

$\hookrightarrow \sf \: 341 - 287 {m}^{2}$

$\hookrightarrow \sf \: 54 {m}^{2}$

Length of 1 m of carpet = 1 × 0.82 = 0.82 m^2

$\star \: \sf \cancel \dfrac{287}{0.82} \: m$

$\hookrightarrow \sf \: 350 \: m \: of \: carpet$

_________________

$\star \tt \: Cost \: of \: fencing = \\ \tt Length \: of \: carpet × rate$

$\hookrightarrow \sf \: 350 \times 124$

$\hookrightarrow \sf \: Rs \: 43400$

Answer 2

Answer:

• Total cost of fencing of carpet = Rs. 43400

Step-by-step explanation:

Given:

• Length of rectangular hall = 22 m
• Breadth of rectangular hall = 15.5 m
• Margin of carpet = 75 cm = 0.75 m
• Visit of carpet = 82 cm = 0.82 m
• Cost of fencing = Rs. 124 per meter

To Find:

• Total cost of fencing.

$\rule{150}{2}$

Now, firstly we will calculate area of hall,

⇒ Area of rectangular hall = length × breadth

⇒ Area of rectangular hall = 22 × 15.5

⇒ Area of rectangular hall = 341 m²

$\rule{150}{2}$

Now, margin we have to given that is 0.75 m. So, from this we will calculate dimension of carpet.

⇒ Length of carpet = (Length of rectangular hall - 2 × 0.75)

⇒ Length of carpet = (22 - 2 × 0.75)

⇒ Length of carpet = (22 - 1.5)

⇒ Length of carpet = 20.5 m

$\rule{150}{1}$

⇒ Breadth of carpet = (Breadth of rectangular hall - 2 × 0.75)

⇒ Breadth of carpet = (15.5 - 2 × 0.75)

⇒ Breadth of carpet = (15.5 - 1.5)

⇒ Breadth of carpet = 14 m

$\rule{150}{2}$

Now, we will calculate area of carpet,

⇒ Area of carpet = Length × Breadth

⇒ Area of carpet = 20.5 × 14

⇒ Area of carpet = 287 m²

$\rule{150}{2}$

Now, we know that,

⇒ Left area = Area of hall - Area of carpet

⇒ Left area = 341 m² - 287 m²

⇒ Left area = 54 m²

$\rule{150}{1}$

⇒ Length of 1 m of carpet = 1 m × 0.82 m

⇒ Length of 1 m of carpet = 0.82 m²

⇒ 287/0.82 = 350 m of carpet.

$\rule{150}{2}$

Now, cost of fencing of carpet = Rs. 124 per meter.

So, cost of fencing on 350 m of carpet = Rs. 124 × 350

                                                            = Rs. 43400

Hence, total cost of fencing of carpet = Rs. 43400

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