hardwick744

09.04.2020 •

Mathematics

– 4/9 (18 – 17) is equivalent to which value?

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Ответ:

ottie123

24.12.2022

Mathematics

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.

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