contestada

A designer enlarged both the length and the width of a rectangular carpet by 60 percent. The new carpet was too large so the designer was asked to reduce its length and its width by 25 percent. By what percent was the area of the final item greater than the area of the original?
(A) 20% (B) 35% (C) 44% (D) 82% (E) 85%

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%



deepakrai138

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%

Otras preguntas