The area of a square game board is 144 sq. in. What's the length of the sides of the board?
A. 8 in.
B. 72 in.
C. 36 in.
D. 12 in.
Answer (1)
Define the side length of the square as s and recall the area formula A = s 2 .
Substitute the given area A = 144 into the formula: 144 = s 2 .
Solve for s by taking the square root of both sides: s = 144 .
Determine the side length: 12 in.
Explanation
Problem Analysis We are given that the area of a square game board is 144 sq. in. We need to find the length of the sides of the board.
Area Formula Let s be the length of a side of the square game board. The area A of a square is given by the formula: A = s 2 We are given that the area A = 144 sq. in.
Substitute and Solve Substitute the given area into the formula: 144 = s 2 To find the side length s , we need to take the square root of both sides of the equation: s = 144
Calculate the Square Root The square root of 144 is 12, so: s = 12 Since the side length must be positive, we take the positive square root. Therefore, the length of the side of the square game board is 12 inches.
Final Answer The length of the sides of the board is 12 inches. Therefore, the correct answer is D.
Examples
Understanding the area of squares is useful in many real-life situations. For example, if you're planning to install square tiles in a room, knowing the area of the room helps you determine how many tiles you need. If each tile has an area of 1 square foot and your room is a square with sides of 10 feet, the room's area is 10 × 10 = 100 square feet, so you'll need 100 tiles. This concept is also used in gardening when planning square garden beds or in construction when calculating the area of square foundations.
