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?

#("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")#
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#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

#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 :)

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#