Question

Each tile has length 1/3 in. And width 1/4 in. The actual tiles have length 1/4 ft and width of 3/16 ft. What is the ratio of the length of a tile in the model to the lenfth of an actual tile? What is the ratio of the area of a tile the model to the area of an actual tile? Describe two ways to find each ratio

Answer 1

Given:

Model tile length = $\dfrac{1}{3}\text{ in.}$

Model tile width = $\dfrac{1}{4}\text{ in.}$

Actual tile length = $\dfrac{1}{4}\text{ ft.}$

Actual tile width = $\dfrac{3}{16}\text{ ft.}$

To find:

The ratio of the length of a tile in the model to the length of an actual tile and the ratio of the area of a tile the model to the area of an actual tile.

Solution:

We know that,

1 ft = 12 in.

Actual tile length $=\dfrac{1}{4}\times 12\text{ in.}$

                             $=3\text{ in.}$

Actual tile width $=\dfrac{3}{16}\times 12\text{ in.}$

                           $=\dfrac{3}{4}\times 3\text{ in.}$

                           $=\dfrac{9}{4}\text{ in.}$

The ratio of the length of a tile in the model to the length of an actual tile is

$\dfrac{\dfrac{1}{3}}{3}=\dfrac{1}{9}=1:9$

Therefore, the ratio of the length of a tile in the model to the length of an actual tile is $\dfrac{1}{9}$ or it can be written as 1:9.

Area of rectangle = length × width

Area of model tile $=\dfrac{1}{3}\times \dfrac{1}{4}$

                               $=\dfrac{1}{12}\text{ in.}^2$

Area of actual tile $=3\times \dfrac{9}{4}$

                               $=\dfrac{27}{4}\text{ in.}^2$

The ratio of the area of a tile the model to the area of an actual tile is

$\dfrac{\dfrac{1}{12}}{\dfrac{27}{4}}=\dfrac{1}{12}\times \dfrac{4}{27}$

$\dfrac{\dfrac{1}{12}}{\dfrac{27}{4}}=\dfrac{1}{3}\times \dfrac{1}{27}$

$\dfrac{\dfrac{1}{12}}{\dfrac{27}{4}}=\dfrac{1}{81}=1:81$

Therefore, ratio of the area of a tile the model to the area of an actual tile is $\dfrac{1}{81}$ or it can be written as 1:81.