Question 54370
" one square is 3 units larger per side then the other, find the sizes of the squares."
:
Small square side = x; then larger square side = (x+3)
:
:
"The sum of the areas of two squares is 225".
: 
   x^2 + (x+3)^2 = 225
:
x^2 + (x^2 + 6x + 9 = 225;  FOILed (x+3)^2
:
x^2 + x^2 + 6x + 9 - 225  = 0
:
2x^2 + 6x - 216 = 0
:
x^2 + 3x - 108 = 0; Simplified, divide equation by 2
:
Factors to:
(x + 12)(x - 9) = 0
:
x = +9, positive solution is what we want here
:
:
Check:
x^2 + (x+3)^2 = 225
9^2 + (9+3)^2 =
81  +  144  = 225