Question

The rectangle below has an area of 4(x+3) [4 is width, x+3 is length] square units. When the dimensions of the rectangle are doubled, the area of the new rectangle in terms of x is 8(2x+6). [ 8 being the width and 2x+6 being the length.] Will the ratio of the area of the original rectangle to the larger rectangle be the same for any positive value of x?

Answer 1

Yes it will be. The ratio will always be

4(x+3)/8(2x+6)
4x+12/16x+48

ratio = 1/4

You can test this out by substituting some values of x.

For example,

x=1
Orig=16 New=64
16/64=1/4

x=2
Orig=20 New=80
20/80=1/4

and so on...