Which represents a side length of a square that has an area of 450 square inches?
$15 \sqrt{2} \text{ in}$.
$15 \sqrt{3} \text{ in}$.
112.5 in .
115.5 in.
Answer (2)
The area of the square is given as 450 square inches.
The side length s of the square is found by taking the square root of the area: s = 450 .
Simplify the square root: s = 225 × 2 = 15 2 .
The side length of the square is 15 2 in .
Explanation
Problem Analysis The problem states that the area of a square is 450 square inches, and we need to find the side length of this square. We know that the area of a square is given by the formula A = s 2 , where A is the area and s is the side length. Therefore, to find the side length, we need to take the square root of the area.
Applying the Area Formula We are given that the area A = 450 square inches. To find the side length s , we use the formula $s = A Substituting the given area, we have s = 450
Simplifying the Square Root Now, we simplify the square root. We can factor 450 as 450 = 225 × 2 . Therefore, s = 225 × 2 Since 225 = 15 , we can write s = 225 × 2 = 15 2 So, the side length of the square is 15 2 inches.
Final Answer The side length of the square is 15 2 inches. Comparing this to the given options, we see that the correct answer is 15 2 in.
Examples
Imagine you're designing a square garden and you know you want it to cover an area of 450 square feet. To determine how much fencing you need, you must calculate the length of each side. By finding the square root of the area, you can determine that each side should be approximately 15 2 feet long. This ensures you purchase the correct amount of fencing to enclose your garden perfectly.
The side length of a square with an area of 450 square inches is calculated to be 15 2 in . Thus, the correct answer is 15 2 in .
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