Question 4756: if a rectangle has an area of 100 and 1 side is 2 feet longer then the other what are the length of the second side? Answer by longjonsilver(2297) (Show Source):
Area of rectangle is x(x+2) = 100, so we get . This does not factorise easily, so use the quadratic formula or complete the square (basically the same thing)...
--> 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:
so now we can take square root of both sides, remembering there are 2 answers:
or
so --ignore the other answer as this is physically not correct for a length.
Longer side is -->
you can check your answer by multiplying by to see if they equal 100.
