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: [tex] x^{2} + x^{2} +6x+9=425[/tex] which simplifies a bit to [tex]2 x^{2} +6x+9=425[/tex]. 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. [tex]2 x^{2} +6x-416=0[/tex]. 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.
