Final answer:
To find the line segment length from the area of a square, take the square root of the area. For example, if a square has an area of 16 square units, the length of one side and the line segment is the square root of 16, which is 4 units. Option D
Step-by-step explanation:
To find the length of a line segment by using the area of a square when the line segment is a side of the square, we must use the relationship between the area of the square and the length of its sides. A square's area is found by squaring (multiplying by itself) the length of one side. If the area of the square is known, then to find the length of a side (and therefore, the length of the line segment), we take the square root of the area.
For example, if we know that the area of a square is 16 square units, to find the length of one side (which is also the length of the line segment we started with), we calculate the square root of the area. In mathematical terms:
Area of square = side length × side length = s²
To find side length (s), we take √(Area of square)
So, s = √16 = 4 units
Therefore, the correct method to find the length of the line segment is to take the square root of the area of the square.
If we look at the options provided in the question, the correct answer is:
(D) Take the square root of the area of the square.
In terms of scaling and comparing areas, when dealing with a square that is scaled up, the areas increase quadratically. In the example provided with Marta's squares:
The side length of the larger square is 4 inches × 2 = 8 inches.
The area of the smaller square is 4 inches × 4 inches = 16 square inches.
The area of the larger square is 8 inches × 8 inches = 64 square inches.
Thus, the area of the larger square is four times that of the smaller square. Option D