Which represents a side length of a square that has an area of 450 square inches?
A. 15√5 m.
B. 112.5 in
C. 115.5 in
The Correct Answer and Explanation is:
To determine the side length of a square with an area of 450 square inches, we need to recall the formula for the area of a square:
[
\text{Area} = \text{side length}^2
]
Let the side length of the square be represented as ( s ). Since we know that the area is 450 square inches, we can set up the equation:
[
s^2 = 450
]
Now, to find the side length ( s ), we take the square root of both sides of the equation:
[
s = \sqrt{450}
]
We can simplify the square root of 450. First, factor 450 into prime factors:
[
450 = 9 \times 50
]
[
9 = 3^2 \quad \text{and} \quad 50 = 2 \times 5^2
]
Thus,
[
\sqrt{450} = \sqrt{9 \times 50} = \sqrt{9} \times \sqrt{50} = 3 \times \sqrt{50}
]
Next, simplify ( \sqrt{50} ). We know that ( 50 = 25 \times 2 ), so:
[
\sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2} = 5\sqrt{2}
]
Therefore,
[
\sqrt{450} = 3 \times 5\sqrt{2} = 15\sqrt{2}
]
Now, let’s approximate ( \sqrt{2} \approx 1.414 ):
[
15\sqrt{2} = 15 \times 1.414 \approx 21.21
]
Thus, the side length of the square is approximately 21.21 inches.
Now, let’s examine the answer choices:
- A. 15√5 m: This option gives a side length in meters and does not match the calculated value or the required units of inches.
- B. 112.5 in: This option does not match the calculated value of 21.21 inches.
- C. 115.5 in: This option also does not match the calculated value.
None of the provided answer choices are correct based on the calculated side length. However, based on the closest reasonable unit conversion from the correct side length of ( \approx 21.21 ) inches, it’s likely that additional options or a correction are needed to provide the accurate answer.