Question

The area of the two adjacent walls of a room is 72 m². If the length of the room is twice its
width and the height is 4 m, then find the area of the floor.
[HINT: Area of the 2 adjacent walls = (length+breadth) * height]​

Answer 1

Step-by-step explanation:

Solution :-

Let the width of the room be w m

Then, the length of the room

= twice its breadth

= 2w m

Length of the room = 2w m

Given that

Height of the room = 4 m

We know that

The area of a two adjacent walls of the room = (length +breadth)×height sq.units

Area of the two adjacent walls of the given room

=> A = (2w+w)×4 m²

=> A = 3w×4 m²

=> A = 12w m²

According to the given problem

The area of the two adjacent walls of a room

= 72 m²

=> 12w = 72

=> w = 72/12

=> w = 6 m

Width of the room = 6 m

Length of the room = 2w = 2×6 = 12 m

Now

Area of the floor of a room = length×breadth sq.units

Area of the floor of the given room

= 12×6 = 72 m²

Answer:-

Area of the floor of the given room

= 72 m²

Check :-

If length = 12 m width = 6 m and height = 4 m then

The area of the two adjacent walls of a room

=> (12+6)×4 m²

=> 18×4 m²

=> 72 m²

Verified the given relations in the given problem.

Used formulae:-

→ The area of a two adjacent walls of the room A = (length +breadth)×height

sq. units

→ Area of the floor of a room = length×breadth sq.units

Points to know:-

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

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

Answer 2

Answer:

➲ $\\ \textbf {the area of the floor of the room is 72m²}$

Step-by-step explanation:

Given information

1. ↠ Area of the adjacent walls of a room is 72m²
2. ↠ The length of the room is twice width
3. ↠ the height is 4m

What we have to calculate

• ↠ We have to calculate Area of the floor?

Let's as find

Let the width of be x m and

As we have given in question that the length of the room is twice its width So,

➲ 2 × x (width)

➲ 2x m _______(1)

Therefore the length of the room is 2x m

___________________________

As we know that the Area of the 2 adjustment walls = (length + width) × height m²

Now putting values in formula

➲ Area of the 2 adjacent walls = ( 2x + x )4 m²

• Adding 2x + x = 3

➲ Area of the 2 adjacent walls = 3x ×4m²

• On multiplying 3x by 4 we get 12x

➲Area of the 2 adjacent walls = 12x m²

• As we given in question that Area of the 2 adjacent walls of a room is 72m² So,

➲ 72 m² = 12x m²

• Transferring sides

➲ x = 72/12 m²

• On Dividing 72 by 12 we get 6

➲ x = 6m²

Hence the width of the room is 6m

Now we will find length by putting value of x in equation 1

➲ length = 2x m

• putting value of x

➲ length = 2(6) m

• Multiplying 2 by 6 we get 12

➲ length = 12m

The length and width of room is 12m & 6m

Now finding Area of floor of a room

As know that Area of floor is Length × width

Putting values

➲ Area of floor of a room = 12 × 6

• On multiplying 12 by 6 we get 72

➲ Area of floor of a room = 72m²