if the dimensions of the rectangle are doubled what is the area of the new rectangle in terms of x

Question

The distributive property of the rectangle is 4(x+3)=x+3

and will the ratio of the area of the original rectangle to the area of the larger rectangle be the same for any positive value of x? Explain

Answer 1

if x and y denote the original dimensions (length and width)  of the rectangle, then its Area=xy. Now we increase both x and y by 3

NewArea=(x+3)(y+3)=xy+3(x+y)+9=Area+3old perimeter +9

 

NewArea/Area=1+3(1/x+1/y)+9/(xy)