Problem 147 - Algebra and Trigonometry

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: Understand the problem

Let's denote the side length of the original square as 'x'. We know that each side of the square increased by 3 inches to form a new square. So, the side length of the new square is \(x+3\) inches. Now, the area of this new square is given as 64 square inches. So, we have a equation: \((x+3)^2 = 64\).

Step 2: Solve the equation

Solving the equation \((x+3)^2 = 64\), we get \(x+3 = \pm 8\). Considering the positive root for the length (since the length cannot be negative), we get \(x+3 = 8\).

Step 3: Calculate the original side length

Now, solve the equation \(x+3 = 8\) for 'x' by subtracting 3 from each side. Thus, \(x = 8 - 3 = 5\). So, the side length of the original square is 5 inches.