Question

the area of four walls of a room is 240 m square if the length of a room is thrice its breadth the height is 2 metre find the area of the floor

Answer 1

Proper Question :

The area of four walls of a room is 240m², if the length of a room is thrice its breadth the height is 2 metre, find the area of the floor ?

Method of Solution :

In this Question It is given that The area of four walls of a room is 240m², Which means Lateral surface of room is Given that.

We know that Lateral surface of room is 2(l + b ) h

Let the required value of Breadth be x ,

Length = 3x metres

Breadth = x metres

Height = 2 metres

Now, Substituting this on Formula!

Lateral surface of room = 2(l + b ) h

➩ 2(3x + x)2 = 240 m²

➩ 2(4x)2 = 240 m²

➩ 4(4x) = 240 m²

➩ 16x = 240 m²

➩ x = 15 m

•°• Length = 3x

✏ Length ➩ 3(15) = 45m²

✏ Breadth ➩ x = 15 metres



Area of the Floor = length × Breadth

➩ Area of the Floor = 45 × 15

➩ Area of the Floor = 675 m²

Hence, Required Value of Area of the Floor is 675 m².

Answer 2

The area of 4 walls of a room (Rectangle) is $240\:m^{2}$

Which means, LSA(Lateral Surface area) of room is  $240\:m^{2}$.

Given :

LSA = $240\:m^{2}$.

Length(l) = $3\timesbreadth(x)$

Height(h) = 2 m

Solution ⇒ We know the formula of LSA  ⇒  2(l+b)h$units^{2}$.

So,  Putting the values in formula :

LSA ⇒ $2(3\timesx+x)h$ = $240\:m^{2}$

⇒ $2(3\timesx+x)h$ = $240\:m^{2}$

⇒ $2(4x)h$ = $240\:m^{2}$  

⇒ $2(4x)2$ = $240\:m^{2}$  

⇒ $4(4x)$ = $240\:m^{2}$  

⇒ $16x$ = $240\:m^{2}$

⇒ $x$ = $\frac{240\:m^{2}}{16m}$  

⇒ $x$ = $\frac{\cancel{240}\:\:^15\:m^{2}}{\cancel{16}\:\:_1}$  

⇒ $x$ = $\frac{15\:m^{1}}{1}$  

⇒ $x$∴ x = 15 m (Found above)

∴ Breadth = x = 15 m

∵Length = 3x = 3×15 = 45 m

∴ area of the floor = l×b ⇒ 45m × 15m (Values found above)

⇒ 675$m^{2}$.

Thanks!