A garden in the shape of a square has an area of 13 square feet. Each side of the garden has a length of √13 feet. Which of the following is the best decimal approximation for the length of each side?
A.
4.5 feet
B.
6.5 feet
C.
3.6 feet
D.
2.6 feet
The correct answer and Explanation is :
To find the best decimal approximation for the length of each side of a square garden with an area of 13 square feet, we start by recalling that the area ( A ) of a square is given by the formula:
[ A = s^2 ]
where ( s ) is the length of each side. Given that the area ( A ) is 13 square feet, we set up the equation:
[ s^2 = 13 ]
To find ( s ), we take the square root of both sides:
[ s = \sqrt{13} ]
Next, we need to approximate ( \sqrt{13} ) to a decimal value.
To estimate ( \sqrt{13} ), we know that ( \sqrt{13} ) falls between two whole numbers. Since:
[ \sqrt{9} = 3 \text{ and } \sqrt{16} = 4 ]
it follows that:
[ 3 < \sqrt{13} < 4 ]
For a more accurate approximation, consider squaring values between 3 and 4.
Testing 3.5:
[ 3.5^2 = 12.25 ]
which is less than 13. Therefore, ( \sqrt{13} ) is greater than 3.5.
Testing 3.6:
[ 3.6^2 = 12.96 ]
which is very close to 13, and thus, ( \sqrt{13} ) is slightly more than 3.6.
Testing 3.7:
[ 3.7^2 = 13.69 ]
which is slightly more than 13. Hence, ( \sqrt{13} ) is between 3.6 and 3.7.
Based on these approximations, the best choice among the given options for the length of each side is closest to:
C. 3.6 feet
Thus, the best decimal approximation for the length of each side of the square garden is approximately 3.6 feet.