Respuesta :
x= length, y=width
Both the length and width were increased by 60% so now they are:
1.6x and 1.6y
Then they were both reduced by 25% so now they are 75%(100-25) of their previous size so they are:
0.75(1.6x) and 0.75(1.6y)
Their area would be length * width so it would be:
0.75(1.6x) * 0.75(1.6y)
Simplified this would be:
1.2x * 1.2y
Simplified more it would be :
1.44xy which is also 144% of xy which is a 44% increase of the original area (xy)
So the answer is:
44%
The correct option is (C) 44% .
Given A designer enlarged both the length and the width of a rectangular carpet by 60 percent.
Let the length of carpet be [tex]x[/tex] and width be [tex]y[/tex].
Since the length and width were increased by 60% so now they are[tex]1.6x[/tex] and [tex]1.6y[/tex].
Further they were both reduced by 25% so now they are remaining 75% (100-25) of their previous size so they are [tex]0.75\times 1.6x[/tex] and [tex]0.75\times 1.6y[/tex] .
We know that area of rectangle = [tex]length\times width[/tex]
So the area of original rectangular carpet = [tex]x\times y=xy[/tex]
Now the area of final rectangular carpet = [tex]x^{2} 0.75\times 1.6x\times 0.75\times 1.6y=1.2x\times 1.2y=1.44xy[/tex]
Area of final rectangular carpet [tex]=1.44xy[/tex]
Now clearly the area of final carpet is greater by 44 percent of the original carpet area.
For more details on percentage calculation follow the link below:
https://brainly.com/question/8011401
1.2x * 1.2y
Simplified more it would be :
1.44xy which is also 144% of xy which is a 44% increase of the original area (xy)
So the answer is:
44%