{"id":170746,"date":"2024-11-19T22:56:27","date_gmt":"2024-11-19T22:56:27","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=170746"},"modified":"2024-11-19T22:56:29","modified_gmt":"2024-11-19T22:56:29","slug":"which-represents-a-side-length-of-a-square-that-has-an-area-of-450-square-inches","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/11\/19\/which-represents-a-side-length-of-a-square-that-has-an-area-of-450-square-inches\/","title":{"rendered":"Which represents a side length of a square that has an area of 450 square inches"},"content":{"rendered":"\n

Which represents a side length of a square that has an area of 450 square inches?<\/p>\n\n\n\n

A. 15\u221a5 m.<\/p>\n\n\n\n

B. 112.5 in<\/p>\n\n\n\n

C. 115.5 in<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

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:<\/p>\n\n\n\n

[
\\text{Area} = \\text{side length}^2
]<\/p>\n\n\n\n

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:<\/p>\n\n\n\n

[
s^2 = 450
]<\/p>\n\n\n\n

Now, to find the side length ( s ), we take the square root of both sides of the equation:<\/p>\n\n\n\n

[
s = \\sqrt{450}
]<\/p>\n\n\n\n

We can simplify the square root of 450. First, factor 450 into prime factors:<\/p>\n\n\n\n

[
450 = 9 \\times 50
]
[
9 = 3^2 \\quad \\text{and} \\quad 50 = 2 \\times 5^2
]<\/p>\n\n\n\n

Thus,<\/p>\n\n\n\n

[
\\sqrt{450} = \\sqrt{9 \\times 50} = \\sqrt{9} \\times \\sqrt{50} = 3 \\times \\sqrt{50}
]<\/p>\n\n\n\n

Next, simplify ( \\sqrt{50} ). We know that ( 50 = 25 \\times 2 ), so:<\/p>\n\n\n\n

[
\\sqrt{50} = \\sqrt{25 \\times 2} = \\sqrt{25} \\times \\sqrt{2} = 5\\sqrt{2}
]<\/p>\n\n\n\n

Therefore,<\/p>\n\n\n\n

[
\\sqrt{450} = 3 \\times 5\\sqrt{2} = 15\\sqrt{2}
]<\/p>\n\n\n\n

Now, let’s approximate ( \\sqrt{2} \\approx 1.414 ):<\/p>\n\n\n\n

[
15\\sqrt{2} = 15 \\times 1.414 \\approx 21.21
]<\/p>\n\n\n\n

Thus, the side length of the square is approximately 21.21 inches.<\/p>\n\n\n\n

Now, let’s examine the answer choices:<\/p>\n\n\n\n