Question

A room is 6 m long and 5 m wide . How many carpets 1.5 m by 1 m will be required to cover it's floor and what will be the cost of the carpets at Rs 80.25 a piece ?​ plz don't spam the answer from Google if anyone does I will report to the Brainly Community .... and when you do the sum plz explain it ... that how you do it and if anyone does like this I will choose the right answer as Brainliest ..!!!​ so solve fst​

Answer 1

Answer :-

$\:\\\large{\underbrace{\underline{\sf{Firstly,\;let's\;understand\;the\;concept\;:-}}}}$

Here the concept of Areas of Rectangle has been used. We are given the dimensions of the Floor of Room. We can find its area. Then we can find the area of the carpet. Area of floor of room gives the area to carpet. Now if we will divide the area of floor of room by area of carpet, we can find the number of carpets required. Then to find total cost we need to multiply the number of carpets into the total cost.

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★ Formula Used :-

$\:\\\large{\boxed{\sf{Area\;of\;Rectangle\;=\;\bf{Length\:\times\:Breadth}}}}$

$\:\\\large{\boxed{\sf{Number\;of\;Carpet\;=\;\bf{\dfrac{Area\;of\;Floor}{Area\;of\;Carpet}}}}}$

$\:\\\large{\boxed{\sf{Total\;cost\;required\;=\;\bf{Number\;of\;Carpets\;\times\;Cost\;of\;Each\;Carpet}}}}$

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★ Question :-

A room is 6 m long and 5 m wide . How many carpets 1.5 m by 1 m will be required to cover it's floor and what will be the cost of the carpets at Rs 80.25 a piece ?

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★ Solution :-

Given,

» Dimensions of floor of room = 6 m × 5 m

» Dimensions of each carpet = 1.5 m × 1 m

» Cost of each Carpet = Rs. 80.25

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~ For the Area of Floor of Room :-

$\:\\\quad\large{\sf{:\longrightarrow\;\;\:Area\;of\;Rectangle_{(Floor)}\;=\;\bf{Length\:\times\:Breadth}}}$

$\:\\\quad\large{\sf{:\longrightarrow\;\;\:Area\;of\;Rectangle_{(Floor)}\;=\;\bf{6\:\times\:5\;\:=\;\:\underline{\underline{30\;\;m^{2}}}}}}$

$\:\\\large{\boxed{\boxed{\tt{Area\;\;of\;\;Floor\;=\;\bf{30\;\;m^{2}}}}}}$

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~ For the Area of Each Carpet :-

$\:\\\quad\large{\sf{:\longrightarrow\;\;\:Area\;of\;Rectangle_{(Carpet)}\;=\;\bf{Length\:\times\:Breadth}}}$

$\:\\\quad\large{\sf{:\longrightarrow\;\;\:Area\;of\;Rectangle_{(Carpet)}\;=\;\bf{1.5\:\times\:1\;\:=\;\:\underline{\underline{1.5\;\;m^{2}}}}}}$

$\:\\\large{\boxed{\boxed{\tt{Area\;\;of\;\;Floor\;=\;\bf{1.5\;\;m^{2}}}}}}$

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~ For the Number of Carpets Required :-

$\:\\\quad\large{\sf{:\longrightarrow\;\;\:Number\;of\;Carpet\;=\;\bf{\dfrac{Area\;of\;Floor}{Area\;of\;Carpet}}}}$

$\:\\\quad\large{\sf{:\longrightarrow\;\;\:Number\;of\;Carpet\;=\;\bf{\dfrac{30}{1.5}\;\:=\;\:\underline{\underline{20\;\;Carpets}}}}}$

$\:\\\large{\boxed{\boxed{\tt{Number\;\;of\;\;Carpets\;\;Required\;=\;\bf{20\;\;Carpets}}}}}$

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~ For the Total cost of carpets :-

$\:\\\large{\sf{Total\;cost\;of\;Carpets\;=\;\bf{20\;\times\;80.25\;\:=\;\:\underline{\underline{Rs.\;\:1605}}}}}$

$\;\\\large{\underline{\underline{\rm{Thus,\;total\;cost\;of\;carpets\;is\;\;\boxed{\bf{Rs.\;\;1605}}}}}}$

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★ More to know :-

$\:\\\tt{\leadsto\;\;\;Area\;\;of\;\;Square\;=\;(Side)^{2}}$

$\:\\\tt{\leadsto\;\;\;Area\;\;of\;\;Circle\;=\;\pi r^{2}}$

$\:\\\tt{\leadsto\;\;\;Area\;\;of\;\;Parallelogram\;=\;Base\:\times\:Height}$

$\:\\\tt{\leadsto\;\;\;Area\;\;of\;\;Triangle\;=\;\dfrac{1}{2}\:\times\:Base\:\times\:Height}$

$\:\\\tt{\leadsto\;\;\;Perimeter\;\;of\;\;Square\;=\;4\:\times\:(Side)}$

$\:\\\tt{\leadsto\;\;\;Perimeter\;\;of\;\;Rectangle\;=\;2\:\times\:(Length\;+\;Breadth)}$

$\:\\\tt{\leadsto\;\;\;Perimeter\;\;of\;\;Circle\;=\;2\pi r}$

$\:\\\tt{\leadsto\;\;\;Area\;\;of\;\;Scalene\;\;Triangle\;=\;\sqrt{s(s\:-\:a)(s\:-\:b)(s\:-\:c)}}$

$\:\\\tt{\leadsto\;\;\;Semiperimeter\;\;of\;\;Triangle,\;(s)\;=\;\dfrac{Sum\;of\;all\;sides,\;(a\:+\:b\:+\:c)}{2}}$

Answer 2

$\underline{\underline{\sf{\maltese\:\:Question}}}$

⭐ A room is 6 m long and 5 m wide . How many carpets 1.5 m by 1 m will be required to cover it's floor and what will be the cost of the carpets at ₹ 80.25 a piece ?​

$\underline{\underline{\sf{\maltese\:\:Given}}}$

• Dimensions of Room's floor : 6 m × 5 m

• Dimensions of Carpet : 1.5 m × 1 m

• Cost of each Carpet = ₹ 80.25

$\underline{\underline{\sf{\maltese\:\:To\:Find}}}$

• No of carpets 1.5 m by 1 m required to cover the floor of the room

• Cost of the carpets at ₹ 80.25 a piece

$\underline{\underline{\sf{\maltese\:\:Answer}}}$

• Number of Carpet = 20

• Cost of the carpets = ₹ 1605

$\underline{\underline{\sf{\maltese\:\:Calculations}}}$

• Area of Floor = Area of Carpet × Number of Carpet

As already Given (Floor Dimensions) :

• Length = 6 m
• Breadth = 5 m

Area of Floor = Area of Carpet × Number of Carpet

⇒ (Length × Breadth) = Area of Carpet × Number of Carpet

⇒ (6 m × 5 m) = Area of Carpet × Number of Carpet

⇒ 6 × 5 m² = Area of Carpet × Number of Carpet

⇒ 30 m² = Area of Carpet × Number of Carpet

As already Given (Carpet Dimensions) :

• Length = 1.5 m
• Breadth = 1 m

⇒ 30 m² = Area of Carpet × Number of Carpet

⇒ 30 m² = (Length × Breadth) × Number of Carpet

⇒ 30 m² = (1.5 m × 1 m) × Number of Carpet

⇒ 30 m² = 1.5 × 1 m² × Number of Carpet

⇒ 30 m² = 1.5 m² × Number of Carpet

Multiplying both sides by 10

⇒ 30 m² × 10 = 1.5 m² × Number of Carpet × 10

⇒ 300 m² = 15 m² × Number of Carpet

Dividing both sides by 15 m²

⇒ 300 m²/15 m² = (15 m² × Number of Carpet)/15 m²

⇒ 300 m²/15 m² = Number of Carpet

⇒ 300/15 = Number of Carpet

⇒ 20 = Number of Carpet

Switch Sides

⇒ Number of Carpet = 20            

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Cost of the carpets = Number of Carpets × Cost Per Piece

⇒ Cost of the carpets = 20 × Cost Per Piece

⇒ Cost of the carpets = 20 × ₹ 80.25

⇒ Cost of the carpets = ₹ 1605

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