If the length of each side of a square is increased by 3 cm , th4e perimeter of the new square is 40 cm more than twice the length of each side of the original square. Find the dimensions of the original square. Each side of the original square measures

Let the length of each side of the original square be \( x \) cm. The new square's side length will be \( x + 3 \) cm. The perimeter of the original square is \( 4x \) and the perimeter of the new square is \( 4(x + 3) = 4x + 12 \). According to the problem, this new perimeter is also equal to \( 2x + 40 \). Setting these two equal gives us the equation: \[ 4x + 12 = 2x + 40 \] Now, solving for \( x \): 1. Subtract \( 2x \) from both sides: \( 2x + 12 = 40 \) 2. Subtract \( 12 \) from both sides: \( 2x = 28 \) 3. Divide by \( 2 \): \( x = 14 \) Thus, each side of the original square measures 14 cm. To provide some context, the perimeter of a square is simply the total distance around it, which is influenced directly by the length of its sides. Knowing the power of algebra can transform what seems complex into manageable equations, helping to unravel the mystery of geometric relationships. And speaking of squares, they’ve been around for centuries, making appearances in architecture, art, and even mathematics! For example, the ancient Egyptians used them meticulously in the construction of pyramids, and today, squares are foundational in everything from city planning to modern design. Isn’t it amazing how a simple shape can bring together history and mathematics?