If the sides of a square are lenthened by 7 cm, the area becomes 121 cm^2. Find the length of a side of the original square

121 cm^2 = (11 cm) ^2

The original smaller square, 7 cm less, must have had a 4 cm side length.

To solve this problem, we can use the formula for the area of a square: Area = side length².

Let's denote the length of a side of the original square as "x" cm.

According to the problem, if we lengthen each side of the square by 7 cm, the new side length will be (x + 7) cm.

The new area of the square is given as 121 cm². So, we can write the equation:

(x + 7)² = 121

To solve for x, we need to simplify and solve the equation.

Expanding (x + 7)², we get: x² + 14x + 49 = 121.

To isolate x², we subtract 121 from both sides of the equation, which gives us: x² + 14x + 49 - 121 = 0.

After simplifying, we have: x² + 14x - 72 = 0.

Now, we can factor this quadratic equation: (x + 18)(x - 4) = 0.

Setting each factor equal to zero, we have two possible values for x: x + 18 = 0 or x - 4 = 0.

Solving for x in each case, we find: x = -18 or x = 4.

Since the length of a side cannot be negative, the only valid solution is x = 4 cm.

Therefore, the length of a side of the original square is 4 cm.