Question

The length of each side of a square is 3 in. more than the length of each side of a smaller square. the sum of the areas of the squares is 425 in squared . find the lengths of the sides of the two squares.

Answer 1

If the sides of the larger square are 3 in more than the sides of the smaller square, then the measure of the smaller square is x and the larger is x+3.  Area is side*side.  So the area for the smaller square is x*x or x^2.  The area for the larger is (x+3)(x+3) which is x^2+6x+9.  The sum of these areas is 425.  Here's what that looks like: $x^{2} + x^{2} +6x+9=425$ which simplifies a bit to $2 x^{2} +6x+9=425$.  In order to solve for x we have to get everything on the same side, combine like terms, set the quadratic equal to 0, and then factor.  $2 x^{2} +6x-416=0$.  Plug that into the quadratic formula and you will get x values of 13 and -16.  The two things in math that will never EVER be negative are time and distance/length, so we know that the side length cannot possibly be -16, so it has to be 13.  The length of a side for the smaller square then is 13, and 16 for the larger.