Answer:

[tex] \huge \underline \mathfrak\color{red} {Answer↓} [/tex]

[tex]\huge{\fcolorbox{gold}{Red}{Length=540m}}[/tex]

[tex]\huge{\fcolorbox{gold}{lightblue}{360m}}[/tex]

Step-by-step explanation:

Given,

Height of the room = 4.5m

Ratio of length to breadth = 3:2

Rate of decorating its walls = ₹4.50/m²

Total cost of decorating its walls = ₹4050

To Find,

Length and Breadth of the room.

Procedure,

[tex]area \: of \: the \: walls = \frac{4050}{4.5} m ^{2} \\ = 900 {m}^{2} [/tex]

Given that ratio of length to breadth = 3:2

[tex]total \: parts = 3 + 2 \\ = 5[/tex]

Let the length and breadth of the room be 3x and 2x respectively.

[tex] 3x + 2x = 900 [/tex]

[tex]5x = 900[/tex]

[tex]x = \frac{900}{5} [/tex]

[tex]x = 180[/tex]

[tex]length = 3x \\ \: \: \: \: \: \: \: \: = 3 \times 180 \\ = 540[/tex]

[tex]breadth = 2 x \\ \: \: \: \: \: \: \: \: = 2 \times 180 \\ = 360[/tex]