Question

An embroidered placemat cost $2.95. An embroidered tablecloth is similar to the placemat. The ratio of the corresonding sides is 1:4. How much would you expect to pay for the tablecloth?

Answer 1

We would expect to pay $ 47.2 for the tablecloth.

Explanation:

Given,

The ratio of the corresponding sides the embroidered place-mat and the embroidered tablecloth of the is 1:4,

Since, the embroidered tablecloth is similar to the place-mat.

By the property of similar figures,

The ratio of the area of embroidered place-mat and the area of embroidered tablecloth

= ( Ratio of their corresponding sides )²

`=((1)/(4))^2`

`=(1)/(16)`

Let x be the cost of embroidered tablecloth,

The ratio of the cost of embroidered place-mat and the cost of embroidered tablecloth =
`(2.95)/(x)`

We can write,

`(1)/(16)=(2.95)/(x)`

`\implies x = 2.95* 16=47.2`

Hence, We would expect to pay $ 47.2 for the tablecloth.

Answer 2

Given that ratio of sides is 1:4,
then ratio of areas is 1:16
In terms of area tablecloth is 16 X bigger 2.95*16 = 47.20