Question

5.
A door of 2 m by 1 m is fitted in the wall of a
room. The length and the breadth of the wall
are 5.4 m and 3.2 m, respectively. Find the
cost of painting the wall from outside only at
the rate of 150 per square metre.
be​

Answer 1

Answer :-

$\: \\ \quad \: \boxed{\boxed{\rm{\mapsto \: \: \: Firstly \: let's \: understand \: the \: concept \: used}}}$

Here the concept of Area of Rectangle has been used. The side of the wall, is a 2 D plane so we need to find the area only. Firstly we can find the area of the door and then we can subtract it from the area of the wall. And what will be the left area, we can multiply it with the rate. Then we can get final solution.

Let's do it !!

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★ Formula Used :-

$\: \\ \: \large{\boxed{\boxed{\sf{Area \: of \: Rectangle \: \: = \: \: \bf{Length(L) \: \times \: Breadth(B)}}}}}$

$\: \\ \: \large{\boxed{\boxed{\sf{Area \: required \: to \: paint_{(of \: wall)}\:\:=\:\: \bf{Area \: of \: wall \: - \: Area \: of \: door}}}}}$

$\: \\ \: \large{\boxed{\boxed{\sf{Total \: cost \: of \: painting \: = \: \bf{Area \: to \: be \: painted \: \times \: Rate_{(in \: per \: m^{2})}}}}}}$

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★ Question :-

A door of 2 m by 1 m is fitted in the wall of a room. The length and the breadth of the wall are 5.4 m and 3.2 m, respectively. Find the cost of painting the wall from outside only at the rate of 150 per square metre.

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★ Solution :-

Given,

» Dimensions of the Door = 2 m and 1 m

» Dimensions of the Wall = 5.4 m and 3.2 m

» Rate of painting = Rs. 150 per m²

~ For the Area of Wall :-

$\: \\ \qquad \: \large{\sf{\Longrightarrow \: \: \: Area \: of \: Rectangle \: \: = \: \: \bf{Length(L) \: \times \: Breadth(B)}}}$

$\: \\ \qquad \: \large{\sf{\Longrightarrow \: \: \: Area \: of \: Rectangle_{(rectangular \: wall)}\: \: = \: \: \bf{5.4 \: m \: \times \: 3.2 \: m \: \: = \: \: \underline{\underline{17.28 \: m^{2}}}}}}$

$\: \\ \: \large{\boxed{\boxed{\tt{Area \:\: of \:\: Wall \: \: = \: \bf{17.28\: m^{2}}}}}}$

~ For the Area of Door :-

$\: \\ \qquad \: \large{\sf{\Longrightarrow \: \: \: Area \: of \: Rectangle \: \: = \: \: \bf{Length(L) \: \times \: Breadth(B)}}}$

$\: \\ \qquad \: \large{\sf{\Longrightarrow \: \: \: Area \: of \: Rectangle_{(rectangular \: door)}\: \: = \: \: \bf{2 \: m \: \times \: 1 \: m \: \: = \: \: \underline{\underline{2 \: m^{2}}}}}}$

$\: \\ \: \large{\boxed{\boxed{\tt{Area \:\: of \:\: Door \: \: = \: \bf{2 \: m^{2}}}}}}$

~ For the Area to be Painted :-

$\: \\ \qquad \: \large{\sf{\Longrightarrow \: \: \: Area \: required \: to \: paint_{(of \: wall)}\:\:=\:\: \bf{Area \: of \: wall \: - \: Area \: of \: door}}}$

$\: \\ \qquad \: \large{\sf{\Longrightarrow \: \: \: Area \: required \: to \: paint_{(of \: wall)}\:\:=\:\: \bf{17.28 \: m^{2}\: - \: 2 \: m^{2} \: \: = \: \: \underline{\underline{15.28 \: m^{2}}}}}}$

$\: \\ \: \large{\boxed{\boxed{\tt{Area \:\: to \:\: be \: \: painted\: \: = \: \bf{15.28\: m^{2}}}}}}$

~ Total Cost of Painting :-

$\: \\ \: \large{\sf{\Longrightarrow \: \: \: Total \: cost \: of \: painting \: = \: \bf{Area \: to \: be \: painted \: \times \: Rate_{(in \: per \: m^{2})}}}}$

$\: \\ \: \large{\sf{\Longrightarrow \: \: \: Total \: cost \: of \: painting \: = \: \bf{15.28\: m^{2} \: \times \: 150 \: per \: m^{2} \: \: = \: \underline{\underline{Rs. \: 2292}}}}}$

$\: \: \\ \large{\underline{\underline{\sf{\leadsto \: \: Thus, \: total \: cost \: of \: painting \: the \: wall \: is \: \: \boxed{\bf{Rs. \: 2292}}}}}}$

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$\: \underbrace{\large{\rm{Let's \: understand \: more \: Formulas\: :-}}}$

• Area or Square = (Side)²

• Area of Circle = πr²

• Area of Triangle = ½ × Base × Height

• Area of Parallelogram = Base × Height

• Perimeter of Rectangle = 2(Length + Breadth)

• Perimeter of Square = 4 × (Side)

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Answer 2

Given :

A door of 2 m by 1 m is fitted in the wall of a  room. The length and the breadth of the wall  are 5.4 m and 3.2 m, respectively.

To find :

Find the  cost of painting the wall from outside only at  the rate of 150 per square metre.

Solution :

Given, length and breadth of wall = 5.4 m and 3.2 m

∴ Area of wall = 5.4 * 3.2

∴ Area of wall = 17.28 m²

Now, length and breadth of door = 2 m by 1 m

∴ Area of wall = 2 * 1

∴ Area of wall = 2 m²

Now as the wall should be painted from outside so it will be painted without the door.

∴ Area of wall to be painted = Area of wall - Area of door

⇒ Area to be painted = 17.28 - 2

⇒ Area to be painted = 15.28 m²

Now cost of painting the wall :

⇒ Cost of painting = Area to be painted * Rate

⇒ Cost of painting = 15.28 * 150

⇒ Cost of painting = Rs. 2292

Therefore,

Cost of painting the wall from outside = Rs. 2292