# 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?

Apr 3, 2018

$\text{d) } 12 \frac{3}{8}$

#### Explanation:

$\left(\text{drawing " : " actual")-> color(white)("dddd")(1" cm ":color(white)("d")2 3/4 "feet}\right)$

On the drawing we have $4 \frac{1}{2}$ cm so multiply everything by $4 \frac{1}{2}$

$\textcolor{w h i t e}{\text{dddddddddddddddd")->color(white)("ddd")4 1/2 (1" cm ":color(white)("d")2 3/4 "feet}}$

$\textcolor{w h i t e}{\text{dddddddddddddddd")->color(white)("dddd") (4 1/2" cm ":color(white)("d")12 3/8 "feet}}$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Quick check by estimation}}$

Discard the 3/4 from $2 \frac{3}{4} \to 4 \frac{1}{2} \times 2 = 8 + 1 = 9$

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

Apr 4, 2018

$1 \text{cm}$ color(white)(irepresents color(white)(i $2 \frac{3}{4} \text{feet }$

i. e. $1 \text{ cm" -> 2 3/4 "feet }$

$\implies 4 \frac{1}{2} \text{ cm" -> 2 3/4 xx 4 1/2 "feet }$

Solving $2 \frac{3}{4} \times 4 \frac{1}{2}$,

$\implies \frac{11}{4} \times \frac{9}{2} = \frac{99}{8}$

$\implies 12 \frac{3}{8} \text{feet }$

Therefore, option d is the right one :)

Apr 4, 2018

$12 \frac{3}{8} f t$
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:

$x = \frac{2 \frac{3}{4} \times 4 \frac{1}{2}}{1}$

$x = \frac{11}{4} \times \frac{9}{2}$

$x = \frac{99}{8}$

$x = 12 \frac{3}{8} f t$