Problem 148 - College Algebra Essentials

Question

Each side of a square is lengthened by 2 inches. The area of this new, larger square is 36 square inches. Find the length of a side of the original square.

Step-by-Step Solution

Answer

The length of a side of the original square is 4 inches.

Step 1: Understand the relationship between the sides and the area of the square

The area of a square is given by the formula \(A = s^2\), where \(s\) is the length of a side of the square.

Step 2: Write an equation using the given information

Each side of the original square is lengthened by two inches to form a new square which has an area of 36 square inches. Therefore, the square of the length of the side of the larger square is equal to 36: \((s + 2)^2 = 36\).

Step 3: Solve for the value of the original side length

This equation can be rewritten as \(s^2 + 4s + 4 = 36\). Simplifying, we get \(s^2 + 4s - 32 = 0\). Solving this quadratic equation, we have \(s = 4\) or \(s = -8\). However, the length of a side cannot be negative, so the only solution is \(s = 4\). Thus, the original square had sides of length 4 inches.