Question

Christa has a rectangular rug in her living room that is 6 feet wide and 8 feet long. She decides that the rug is too small for the room, so she orders a new one that covers twice as much area. If the new rug is 1.5 times as wide as the original rug, how long, in feet, is the new rug?

Answer 1

The length of the new rug is approximately 10.67 feet.

Step-by-step explanation:

To find the length of the new rug, we need to first find the area of the original rug. The area of a rectangle can be found by multiplying its length and width, so the area of the original rug is 6 feet x 8 feet = 48 square feet. Since the new rug covers twice as much area, its area will be 48 square feet x 2 = 96 square feet.

Next, we need to find the width of the new rug. The new rug is 1.5 times as wide as the original rug, so its width will be 1.5 x 6 feet = 9 feet.

Finally, we can use the area and width of the new rug to find its length. Divide the area of the new rug by its width: 96 square feet ÷ 9 feet = 10.67 feet. Therefore, the length of the new rug is approximately 10.67 feet.

Answer 2

Given:

A rectangular rug in her living room that is 6 feet wide and 8 feet long.

She orders a new one that covers twice as much area.

New rug is 1.5 times as wide as the original rug.

To find:

The length of new rug.

Solution:

We have,

Length of rug = 8 feet

Width of rug = 6 feet

Area of rug is

`Area=length * width`

`A_1=8 * 6`

`A_1=48\text{ sq. feet}`

Area of new rug is twice of area of original rug.

`A_2=2* A_1`

`A_2=2* 48`

`A_2=96\text{ sq. feet}`

New rug is 1.5 times as wide as the original rug.

Width of new rug = 1.5 × 6 = 9 feet

Let the length of new rug be x feets. So, area of new rug is

`A_2=x* 9`

`96=x* 9`

Divide both sides by 9.

`(96)/(9)=x`

`(32)/(3)=x`

`x=\approx 10.67\text{ feet}`

Therefore, the length of new rug is about 10.67 feet.