Question 4756
Let shorter length = x
so longer length = x+2


Area of rectangle is x(x+2) = 100, so we get {{{x^2 + 2x - 100 = 0}}}. This does not factorise easily, so use the quadratic formula or complete the square (basically the same thing)...


{{{x^2 + 2x = 100}}}
{{{x^2 + 2x + 1 = 100 + 1}}} --> are you OK that this is the same as the previous line?. The reason for adding the 1 is that the lefthand side can now be factorised nicely to (x+1)^2, so:


{{{(x+1)^2 = 101}}} so now we can take square root of both sides, remembering there are 2 answers:


{{{(x+1) = +sqrt(101)}}} or {{{(x+1) = -sqrt(101)}}}


so {{{x = -1+sqrt(101)}}} --ignore the other answer as this is physically not correct for a length.


Longer side is {{{2+ -1+sqrt(101)}}} --> {{{1+sqrt(101)}}}


you can check your answer by multiplying {{{-1+sqrt(101)}}} by {{{1+sqrt(101)}}} to see if they equal 100.


jon.