Question

The length and breadth of a room are in the ratio 3:2. The area of the floor is
19.44 m2. Find the dimensions of the room if the area of four walls is 81 m².​

Answer 1

Given :-

• The length and breadth of a room are in the ratio 3:2.

• The area of the floor is 19.44 m².

• The area of four walls is 81 m².

To find :-

The dimensions of the room .

Solution :-

Given that

The ratio of the length and breadth of a room

= 3:2

Let they be 3X m and 2X m

The length of the room (l) = 3X m

The breadth of the room (b) = 2X m

We know that

Area of a rectangle = length ×breadth sq.units

The area of the floor of the room

= 3X×2X m²

= 6X² m²

According to the given problem

The area of the floor = 19.44 m²

=> 6X² = 19.44

=> X² = 19.44/6

=> X² = 3.24

=> X = ± √3.24

=> X = ±√(324/100)

=> X = ±18/10

=> X = ±1.8

Since, The length can't be negative.

Therefore, X = 1.8 m

If X = 1.8 m then length = 3X m

= 3(1.8)

= 5.4 m

If X = 1.8 m then breadth = 2X m

= 2(1.8)

= 3.6 m

Now,

We have,

Length of the floor of the room = 5.4 m

Breadth of the floor of the room = 3.6 m

We know that

Area of the four walls of a room = 2h(l+b) sq.units

Area of the given four walls of the room = 81 m²

=> 2h(l+b) = 81

=> 2h(5.4+3.6) = 81

=> 2h(9) = 81

=> 18h = 81

=> h = 81/18

=> h = 9/2

=> h = 4.5 m

Therefore, Height = 4.5 m

Answer :-

Length of the room = 5.4 m

Breadth of the room = 3.6 m

Height of the room = 4.5 m

Used formulae:-

• Area of a rectangle = length ×breadth sq.units

• Area of the four walls of a room = 2h(l+b) sq.units

• l = length
• b = breadth
• h = height

Answer 2

Given

• The length and breadth of a room are in the ratio of 3 : 2.
• The area of the floor is 19.44 m².
• The area of four walls is 81 m².

To Find :-

• What is the dimensions of the room.

Formula Used :-

$\clubsuit$ Area Of Rectangle Formula :

$\small \bigstar \: \: \sf\boxed{\bold{\pink{Area_{(Rectangle)} =\: Length \times Breadth}}}\: \: \: \bigstar$

Solution :-

First, we have to find the length and breadth of a room :

Let,

$\mapsto \bf Length_{(Room)} =\: 3x\: m$

$\mapsto \bf Breadth_{(Room)} =\: 2x\: m$

Given :

• Area of the floor = 19.44 m²

According to the question by using the formula we get,

$\small \implies \sf\bold{\blue{Area_{(Rectangle)} =\: Length \times Breadth}}$

$\implies \sf 19.44 =\: 3x \times 2x$

$\implies \sf 19.44 =\: 6x^2$

$\implies \sf \dfrac{19.44}{6} =\: x^2$

$\implies \sf 3.24 =\: x^2$

$\implies \sf \sqrt{3.24} =\: x$

$\implies \sf 1.8 =\: x$

$\implies \sf\bold{\green{x =\: 1.8}}$

Hence, the required length and breadth of a room are :

$\dag$ Length Of Room :

$\dashrightarrow \sf Length_{(Room)} =\: 3x\: m$

$\dashrightarrow \sf Length_{(Room)} =\: (3 \times 1.8)\: m$

$\dashrightarrow \sf\bold{\red{Length_{(Room)} =\: 5.4\: m}}$

$\dag$ Breadth Of Room :

$\dashrightarrow \sf Breadth_{(Room)} =\: 2x\: m$

$\dashrightarrow \sf Breadth_{(Room)} =\: (2 \times 1.8)\: m$

$\dashrightarrow \sf\bold{\red{Breadth_{(Room)} =\: 3.6\: m}}$

Now, we have to find the height :

Let,

$\mapsto \bf Height_{(Room)} =\: h\: m$

Given :

• The area of four walls of a room = 81 m²
• Length of room = 5.4 m
• Breadth of room = 3.6 m

According to the question by using the formula we get,

$\small \implies \sf\bold{\blue{Area\: of\: Four\: Walls_{(Room)} =\: 2 \times (l + b) \times h}}$

$\implies \sf 81 =\: 2 \times (5.4 + 3.6) \times h$

$\implies \sf 81 \times \dfrac{1}{2} =\: 9 \times h$

$\implies \sf \dfrac{81 \times 1}{2} =\: 9h$

$\implies \sf \dfrac{81}{2} =\: 9h$

$\implies \sf 40.5 =\: 9h$

$\implies \sf \dfrac{40.5}{9} =\: h$

$\implies \sf 4.5 =\: h$

$\implies \sf\bold{\purple{h =\: 4.5}}$

Hence, the required height is :

$\dag$ Height Of Room :

$\dashrightarrow \sf Height_{(Room)} =\: h\: m$

$\dashrightarrow \sf\bold{\red{Height_{(Room)} =\: 4.5\: m}}$

$\therefore$ The length, breadth and height of a room is 5.4 m , 3.6 m and 4.5 m respectively.

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