Question

The Johnson’s have a square rug in their living room that is 36 ft2. For Christmas, they are building a dollhouse for their daughter. Its linear dimensions are exactly 60 times smaller than their actual house. In the dollhouse, what are the dimensions of the rug (in inches)? [12 inches in 1 foot]

Answer 1

To find the dimensions of the rug in the dollhouse, calculate the square footage of the dollhouse and then determine the linear dimensions of the rug by multiplying the square root of the rug's footage by 1/60. The dimensions of the rug in the dollhouse would be 1.2 inches in length and 1.2 inches in width.

Step-by-step explanation:

To find the dimensions of the rug in the dollhouse, we need to calculate the square footage of the dollhouse and then determine the linear dimensions of the rug.

The dollhouse is 60 times smaller than the actual house, which means its linear dimensions are 1/60th the size of the actual house.

To find the dimensions of the rug in the dollhouse, we can take the square root of the square footage of the dollhouse and then multiply it by 1/60.

Given that the square footage of the rug is 36 ft², the dimensions of the rug in the dollhouse would be:

• Length: √36 * 1/60 = 6 * 1/60 = 1/10 feet
• Width: √36 * 1/60 = 6 * 1/60 = 1/10 feet

Since there are 12 inches in 1 foot, the dimensions of the rug in the dollhouse would be:

• Length: 1/10 feet * 12 inches/1 foot = 1.2 inches
• Width: 1/10 feet * 12 inches/1 foot = 1.2 inches

Answer 2

1. You have that Tthe square rug in their living room is 36 ft², then, the lenghts of its sides, are:

A=L²
L=√A
L=√36 ft²
L=6 ft

2. There are 12 inches in 1 foot, then:

12 inches----1 ft
x----6 ft

x=6x12
x=72 inches

L=72 inches


3. Its linear dimensions are 60 times smaller than their actual house. Then, you have:

L=(72 inches)(1/60)
L=1.2 inches

What are the dimensions of the rug?

The answer is: 1.2 inches