Question

12) The length of a room is 15 m and its breadth is double
its height. If the area of four walls of the room is 250 sq.m,
breadth of the room is:
A) 5 m
B) 8 m
C) 10 m
D) 19 m​

Answer 1

Given :

The length of a room is 15 m and its breadth is double  its height. If the area of four walls of the room is 250 sq.m.

To find :

Breadth of the room.

Solution :

Let the breadth be 'b' m

∴ Height of room = b/2 m  [∵ Breadth = 2 × Height , ∴ Height = Breadth/2]

As we know,

➻ Area of four walls = 2(l + b) × h

Now putting values,

⇒ 250 = 2(15 + b) × (b/2)

⇒ 250 = (15 + b) × b

⇒ 250 = 15b + b²

⇒ b² + 15b - 250 = 0

⇒ b² + 25b - 10b - 250 = 0

⇒ b(b + 25) - 10(b + 25) = 0

⇒ (b - 10)(b + 25) = 0

⇒ (b - 10) = 0   or,  (b + 25) = 0

⇒ b = 10   or,   b = - 25

∵ Breadth can't be negative.

∴ b = 10 m.

∴ Breadth of the room = 10 m      (Option C)

Answer 2

Answer:

Given :-

• Length of room = 15 m
• Lateral Surface area = 250 m²
• Breadth is double of its height

To Find :-

Breadth and height

Solution :-

Let the breadth be B

Height = B/2

Length = 15

We know that

Area of 4 walls = 2(l + b)h

=> 2(15 + B) B/2 = 250

=> B² + 30/2 = 250

=> B² + 15 = 250

=> Spilting middle term

=> B² + (25B - 10B) - 250 = 0

=> B² + 25B - 10B - 250 = 0

=> (B + 25)(B - 10) = 0

=> B = -25, B = +10

Note :

Breadth can't be negative

B = 10

And,

Height = 10/2 = 5 m