The area of a square is 180 square inches. The measure of one side of the square lies between which of these two consecutive integers?
A. between 11 and 12
B. between 12 and 13
C. between 13 and 14
D. between 14 and 15
The Correct Answer and Explanation is:
To solve this problem, we need to find the length of one side of the square, given that the area of the square is 180 square inches.
Step 1: Formula for the area of a square
The area ( A ) of a square is given by the formula:
[
A = s^2
]
where ( s ) is the length of one side of the square. We are told that the area is 180 square inches, so we can set up the equation:
[
s^2 = 180
]
Step 2: Solving for the side length ( s )
To find ( s ), we need to take the square root of both sides of the equation:
[
s = \sqrt{180}
]
Now, we calculate the square root of 180:
[
\sqrt{180} \approx 13.416
]
Thus, the side length ( s ) is approximately 13.416 inches.
Step 3: Identifying the consecutive integers
Since ( s \approx 13.416 ), we can see that the side length lies between 13 and 14 inches. This means that the measure of the side lies between these two consecutive integers.
Step 4: Conclusion
The correct answer is C. between 13 and 14.
Explanation
We started with the known area of the square, which is 180 square inches, and used the formula for the area of a square to set up the equation ( s^2 = 180 ). Solving for ( s ), we took the square root of 180, resulting in approximately 13.416. This value lies between the integers 13 and 14. Therefore, the measure of one side of the square is between these two consecutive integers, and the correct answer is C.
Understanding this involves recognizing that the square root of a number gives us the length of a side when the area is known. By approximating the square root, we can find the approximate range for the side length.