Question 932584

given: 
 area of a square is {{{256cm^2}}}

Let's represent each side as "{{{x}}}". 
Let's represent the amount added and subtracted as "{{{y}}}".
if amount is removed from one dimension and added to the other, one side of rectangle will be:{{{x-y}}} and other side will be {{{x+y}}}

then the measure of the side of square is {{{sqrt(256cm^2)= 16cm}}} , or the square is  {{{16cm}}} by {{{16cm}}}


 
The equation that can be set up is:

the area of a square is {{{A=x^2=256cm^2}}}

the area of a rectangle is {{{A[r]=(x-y)(x+y)}}}

since the resulting rectangle has an area {{{16cm^2}}} less, we have:

{{{x^2-16cm^2 =(x+y)(x-y) }}}.........solve for {{{x}}}

{{{x^2-16cm^2 =x^2-y^2}}}...............the {{{x^2}}} cancels out leaving us:

{{{-16cm^2 =-y^2}}}.... divide both sides by {{{-1}}} 

{{{16cm^2 =y^2}}}

{{{y=4cm}}}

so, the length of the rectangle is  {{{x+y=16cm+4cm=20cm}}} and
the width of the rectangle is  {{{x-y=16cm-4cm=12cm}}}

Therefore we can solve this rectangle size as {{{20cm}}} by {{{12cm}}}. 

The area comes out to be {{{A[r]=20cm*12cm=240cm^2}}}