Pat needs to order a square carpet with an area of 12 meters-squared. Find the length of each side of the carpet in meters, rounded to two decimal places.
Side length = meters
Answer (1)
The problem provides the area of a square carpet and asks for the side length.
The area of a square is given by A = s 2 , where s is the side length.
Given A = 12 , we find s = 12 = 2 3 .
Approximating to two decimal places, the side length is 3.46 meters.
Explanation
Problem Analysis We are given that Pat needs to order a square carpet with an area of 12 meters-squared. Our goal is to find the length of each side of the carpet, rounded to two decimal places.
Area Formula Let s be the side length of the square carpet in meters. The area of a square is given by the formula: A = s 2 We are given that the area A = 12 square meters. Therefore, s 2 = 12
Solving for Side Length To find the side length s , we take the square root of both sides of the equation: s = 12 We can simplify the square root as follows: s = 4 × 3 = 4 × 3 = 2 3
Approximation Now, we need to approximate the value of 2 3 to two decimal places. The square root of 12 is approximately 3.4641. Rounding this to two decimal places, we get: s ≈ 3.46 meters
Final Answer Therefore, the length of each side of the carpet is approximately 3.46 meters.
Examples
Understanding how to calculate the side length of a square given its area is useful in many real-world scenarios. For example, if you're planning to build a square garden and you know the area you want the garden to cover, you can use this calculation to determine how long each side of the garden should be. This ensures you have enough space for your plants and can plan your garden layout effectively. Knowing the relationship between area and side length helps in efficient space management and planning.
