Answer:
The height of the Mariah's room is 3.12 feet
Explanation:
Given as :
The length of the room = L = 12 feet
The breadth of the room = 11.5 feet
Let The height of room = H feet
The total surface area of room including ceiling and floor = 423 feet²
∵ The total surface area of room including ceiling and floor = 2 × ( Length × Breadth + Length × Height + Width × Height )
So, 2 × ( L × B + L × H + W × H ) = 423
Or, ( 12 × 11.5 + 12 × H + 11.5 × H ) =

Or, ( 12 × 11.5 + 12 × H + 11.5 × H ) = 211.5
Or, ( 12 × H + 11.5 × H ) = 211.5 - 138
Or, H × (12 + 11.5 ) = 73.5
Or, H × 23.5 = 73.5
∴ H =

i.e H = 3.12 feet
So, The height of room = H =3.12 feet
Hence, The height of the Mariah's room is 3.12 feet Answer