Question 113087
Are you sure the area is decreased by 36 square METERS?  36 sq centimeters would make more sense.


If it actually is {{{36m^2}}} like you say, then let x be the length of the side of the original square.


The area of the original square is then {{{x^2}}}.  The area of the new square would then be {{{x^2-36m^2}}}.  But since the length of the side of the new square is {{{x-.02m}}}, , the area of the new square is also {{{(x-.02m)^2}}}


We can now set these two expressions for the area of the new square to be equal.


{{{x^2-36=(x-.02)^2}}}
{{{x^2-36=x^2-.04x+.0004}}}, expand the binomial using FOIL
{{{-36.0004=-.04x}}}, collect terms
{{{x=36.0004/.04=900.01}}}, multiply by -1 and divide by .04


The answer is 900.01 meters.


The problem set up and the equations are the same if you really meant {{{36cm^2}}}.  The only thing that changes are the numbers.


{{{x^2-36=(x-2)^2}}}
{{{x^2-36=x^2-4x+4}}}, expand the binomial using FOIL
{{{-40=-4x}}}, collect terms
{{{x=40/4=10}}}, multiply by -1 and divide by 4


The answer is 10cm.


And to answer your question, no, {{{(x-6)(x+6)}}} has nothing to do with this problem.  That is the correct factorization of the {{{x^2-36}}} expression for the area of the new square, but as you have seen factoring this expression wasn't necessary.


Hope that helps,
John