Question

(vi) The length, breadth and height of a room area in the ratio 3:1:2. If the area of
four walls of the room is 144 m² then its breadth is
(a) 15 m
(b) 12 m
(c) 9 m
(d) 3 m​

Answer 1

✬ Breadth = 3 m ✬

Step-by-step explanation:

Given:

• Length , breadth and height of a room are in ratio of 3 : 1 : 2.
• Area of four walls of room is 144 m².

To Find:

• What is the measure of breadth ?

Solution: Let x be the common in given ratios. Therefore,

• Length = 3x m
• Breadth = x m
• Height = 2x m

As we know that

★ Ar. of 4 walls of room = 2(L + B) × H ★

A/q

• Area of four walls is 144 m².

$\implies{\rm }$ 2(3x + x) × 2x = 144

$\implies{\rm }$ 2(4x) × 2x = 144

$\implies{\rm }$ 8x × 2x = 144

$\implies{\rm }$ 16x² = 144

$\implies{\rm }$ x² = 144/16

$\implies{\rm }$ x² = 9

$\implies{\rm }$ x = 3

So measure of

• Length is 3(3) = 9 m.
• Breadth is 3 m.
• Height is 2(3) = 6 m.

Hence, breadth of room is 3 m.

(Option D is correct)

Answer 2

$\huge\underbrace{\mathbb{ANSWER}}$

$\sf Let \: the \: ratio \: be \: 3x : 1x : 2x$

$\boxed{\rm{CSA \: of \: rectangle = 2 (l+b) h}}$

⟹$\sf ~ 2(3x + x) \times 2x = 144$

⟹$\sf ~ 2(4x) \times 2x = 144$

⟹$\sf ~16 {x}^{2} = 144$

⟹$\sf ~ {x}^{2} = \dfrac{144}{16}$

⟹$\sf~ {x}^{2} = 9$

⟹$\sf ~x = \sqrt{9}$

⟹$\sf ~x = 3$

$\therefore \: \underline{\underline{ \sf{ Breadth \: of \: rectangular \: room \: (x) \: = \red{ 3m}}}}$