Question

An architectural drawing lists the scale as 1/4" = 1'. If a bedroom measures 6 3/4" by 4 1/2" on the drawing, how large is the bedroom?A. 9 ft by 13.5 ftB. 18 ft by 9 ftC. 18 ft by 27 ftD. 72 in. by 108 in

Answer 1

Given a bedroom of the measurement on a scale drawing as

`6(3)/(4)^(\doubleprime)\text{ by 4}(1)/(2)^(\doubleprime)`

On an architectural drawing, the scale is

`(1)/(4)^(\doubleprime)=1^(\prime)`

Converting the measurements of the bedroom into inches,

Where,

`1^(\prime)=12^(\doubleprime)=1ft`
`\begin{gathered} 6(3)/(4)^(\doubleprime)=(27)/(4)^(\doubleprime) \\ 4(1)/(2)^(\doubleprime)=(9)/(2)^(\doubleprime) \end{gathered}`

The measurement of the room will be,

`\begin{gathered} (1)/(4)^(\doubleprime)=1^(\prime)\text{ (on the scale drawing)} \\ (27)/(4)^(\doubleprime)=(27)/(4)*(1)/((1)/(4))=(27)/(4)*(4)/(1)=27^{\prime\text{ }}(i.e\text{ 27ft)} \\ (9)/(2)^(\doubleprime)=(9)/(2)*(1)/((1)/(4))=(9)/(2)*(4)/(1)=18^{\prime\text{ }}(i.e\text{ 18ft)} \end{gathered}`

Recall that,

`1^(\prime)=1ft`

Hence, the answer is option C (18ft by 27ft)