A rectangle has a length of x inches and a width of 2 inches less than the length. If the dimensions were doubled, what would be the area of the new rectangle i

Question

A rectangle has a length of x inches and a width of 2 inches less than the length. If the dimensions
were doubled, what would be the area of the new rectangle in terms of x?

Answer 1

Let A₁ be the area of the original rectangle with length x and width x-2:

 

A₁ = x*(x-2) = x² - 2x

 

Now let A₂ be the area of the rectangle after we double the length to 2x and the width to 2(x-2):

 

A₂ = 2x*2(x-2)

 

= 4x² - 8x

 

= 4(x² - 2x)

 

= 4A₁

 

When you double the dimensions, the area increases by 2² = 4

Answer 2

Length = x                      New Length = 2x                                    

Width = x-2                    New Width = 2(x-2) = 2x-4

 

 

 

                                         New Area = 2x(2x-4) = 4x² - 8x