The area of a square is tripled by adding 10 cm to one dimension and 12 cm to the other. Determine the side length of the square.

Area = length * width

A = x²

3x² = (x+10) (x+12)

3x² = x²+10x+12x+120

3x² = x²+22x+120

3x²-3x² = x²+22x+120-3x²

0 = - 2x²+22x+120

Factor to solve for x:

-2 (x²-11x-60)

(x+4) (x-15)

x = - 4 & x = 15 but we can't have a negative length so we eliminate 4. The length of the square is 15 cm.