Final answer:
The side length of the original square is 12 cm. This is found by solving the equation (x + 4 cm)^2 = 256 cm^2, resulting in x = 12 cm after subtracting the additional length and taking the square root.
Step-by-step explanation:
To find the length of a side of the original square when the sides are lengthened by 4 cm and the area becomes 256 square cm, we first acknowledge that each side of the larger square is the side of the original square plus an additional 4 cm. Since the area of a square is equal to the side length squared, we can set up an equation where (original side length + 4 cm) squared equals 256 square cm.
Let the original side length be x. The equation is (x + 4 cm)2 = 256 cm2. Solving for x, we first take the square root of both sides, which gives us x + 4 cm = 16 cm. Subtracting the additional 4 cm from both sides, we find x = 12 cm. Therefore, each side of the original square is 12 cm long.