Respuesta :
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
[tex]Area=length \times width[/tex]
[tex]A_1=8 \times 6[/tex]
[tex]A_1=48\text{ sq. feet}[/tex]
Area of new rug is twice of area of original rug.
[tex]A_2=2\times A_1[/tex]
[tex]A_2=2\times 48[/tex]
[tex]A_2=96\text{ sq. feet}[/tex]
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
[tex]A_2=x\times 9[/tex]
[tex]96=x\times 9[/tex]
Divide both sides by 9.
[tex]\dfrac{96}{9}=x[/tex]
[tex]\dfrac{32}{3}=x[/tex]
[tex]x=\approx 10.67\text{ feet}[/tex]
Therefore, the length of new rug is about 10.67 feet.
