Question

Mariah’s room has a length of 12 feet, a width of 11.5 feet. She knows that she is covering 423 ft2. What is the height of Mariah’s room?

Answer 1

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 ) =
`(423)/(2)`

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 =
`(73.5)/(23.5)`

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