Question

If the length of the kitchen is 4 1/2 cm on the scale drawing, what is the actual length, in feet of the kitchen?

Answer 1

`"d) "12 3/8`

Explanation:

`("drawing " : " actual")-> color(white)("dddd")(1" cm ":color(white)("d")2 3/4 "feet")`

On the drawing we have `4 1/2` cm so multiply everything by `4 1/2`

`color(white)("dddddddddddddddd")->color(white)("ddd")4 1/2 (1" cm ":color(white)("d")2 3/4 "feet")`

`color(white)("dddddddddddddddd")->color(white)("dddd") (4 1/2" cm ":color(white)("d")12 3/8 "feet")`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Quick check by estimation")`

Discard the 3/4 from `2 3/4->4 1/2xx2 = 8+1=9`

Options a, b and c are too small. They are less than 9 so the answer has to be option d

Answer 2

`1 "cm"` `color(white)(i`represents `color(white)(i` `2 3/4 "feet "`

i. e. `1 " cm" -> 2 3/4 "feet "`

`=> 4 1/2 " cm" -> 2 3/4 xx 4 1/2 "feet "`

Solving `2 3/4 xx 4 1/2`,

`=> 11/4 xx 9/2 = 99/8`

`=> 12 3/8 "feet "`

Therefore, option d is the right one :)

Answer 3

`12 3/8 ft`
Option D

Explanation:

Direct proportion is a great way to work with scales - the conversions are super easy done this way!
Compare the lengths as follows:

`(1cm)/(2 3/4 ft) = (4 1/2cm)/(x ft)" "(larr "scale drawing")/(larr"real size")`
Cross multiply to get:

`x = (2 3/4 xx 4 1/2)/1`

`x = 11/4 xx9/2`

`x = 99/8`

`x = 12 3/8 ft`