Problem 147 - College Algebra Essentials

Question

Each side of a square is lengthened by 3 inches. The area of this new, larger square is 64 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 5 inches.

Step 1: Define the problem

Let x be the length of a side of the original square. Each side of this square is lengthened by 3 inches, therefore the length of the side of the new square is \(x+3\). The area of the new square is 64 square inches. According to the mathematical rule, the area of a square can be found by squaring its side length. So we write the equation \((x+3)^2 = 64\).

Step 2: Solve the equation

To solve the equation, we need to apply the square root to both sides of the equation. Taking the square root of both sides of the equation \((x+3)^2 = 64\) gives us \(x+3 = \pm 8\). We are looking for a length, so we can discard the negative solution.

Step 3: Find the original length

Now, solve the equation \(x+3 = 8\) for \(x\) . Subtract 3 from both sides to isolate \(x\), which gives us \(x = 5\). Therefore, the length of a side of the original square is 5 inches.