Question

2.6.ps-8
an architect makes a model of a new house. the model shows a tile patio in the backyard. in the model, each tile has length (\frac{1}{4}) in. and width (\frac{1}{6}) in. the actual tiles have length (\frac{1}{3}) ft and width (\frac{2}{9}) ft. what is the ratio of the length of a tile in the model to the length of an actual tile? what is the ratio of the area of a tile in the model to the area of an actual tile? use pencil and paper. describe two ways to find each ratio.
the ratio of the area of a tile in the model to the area of an actual tile is (square).
(type the ratio as a simplified fraction.)
enter your answer in the answer box and then click check answer.
all parts showing

Explanation:

Step1: Convert model tile dimensions to feet

Model length: $\frac{1}{4}$ in = $\frac{1}{4\times12}$ ft = $\frac{1}{48}$ ft
Model width: $\frac{1}{6}$ in = $\frac{1}{6\times12}$ ft = $\frac{1}{72}$ ft

Step2: Calculate model tile area

Model area $A_m = \frac{1}{48} \times \frac{1}{72} = \frac{1}{3456}$ sq ft

Step3: Calculate actual tile area

Actual length $l_a = \frac{1}{3}$ ft, actual width $w_a = \frac{2}{9}$ ft
Actual area $A_a = \frac{1}{3} \times \frac{2}{9} = \frac{2}{27}$ sq ft

Step4: Find area ratio (model : actual)

Ratio $= \frac{A_m}{A_a} = \frac{\frac{1}{3456}}{\frac{2}{27}} = \frac{1}{3456} \times \frac{27}{2} = \frac{27}{6912} = \frac{1}{256}$

Answer:

$\frac{1}{256}$