Solve each problem. See Examples 1 and 2. Dimensions of a Square. The length of each side of a square is 3 in. more than the length of each side of a smaller square. The sum of the areas of the squares is 149 in.2. Find the lengths of the sides of the two squares.

Verified step by step guidance

1. Let the side length of the smaller square be $x$ inches.
2. The side length of the larger square is $x+3$ inches.
3. The area of the smaller square is $x^2$ square inches.
4. The area of the larger square is $(x+3{)}^2$ square inches.
5. Set up the equation: $x^2+(x+3{)}^2=149$ and solve for $x$.

Key Concepts

Area of a Square

The area of a square is calculated by squaring the length of one of its sides. If 's' represents the length of a side, the area is given by the formula A = s². Understanding this concept is crucial for solving problems involving squares, as it allows you to relate the side lengths to the total area.

Algebraic Expressions

Algebraic expressions are mathematical phrases that can include numbers, variables, and operations. In this problem, we can express the side lengths of the squares using variables, allowing us to set up equations based on the relationships described in the question. This is essential for translating the problem into a solvable format.

System of Equations

A system of equations consists of two or more equations that share variables. In this scenario, we can create a system based on the relationships between the side lengths and their areas. Solving this system will yield the values of the side lengths for both squares, which is the ultimate goal of the problem.