the area of square varies directly with the square of its side lengt
A = ks^2
In fact,
A = s^2
To determine the relationship between the area of a square and its side length, we can use the concept of direct variation.
Direct variation means that when one quantity increases, the other quantity also increases proportionally. In this case, as the side length of the square increases, the area of the square will also increase.
Let's denote the side length of the square as "s" and the area as "A."
According to the given statement, the area of the square varies directly with the square of its side length. Mathematically, we can express this relationship as:
A ∝ s^2
The symbol "∝" denotes proportionality, meaning that there is a constant of proportionality involved in the relationship.
To determine the exact relationship between the area and the side length, we need to introduce a constant. Let's call this constant "k."
Therefore, we can rewrite the relationship as:
A = k * s^2
Here, "k" represents the constant of proportionality, which will be specific to this particular square.
By squaring the side length (s^2) and multiplying it by the constant (k), we can calculate the area (A) of the square.
To find the area of a square, you need to know the length of its side. In this case, we are given that the area of a square varies directly with the square of its side length. This means that if you increase the side length of the square by a certain factor, the area will increase by that factor squared.
To demonstrate this concept, let's say the side length of the square is represented by "x." According to the given information, we know that the area, which we'll call "A," is directly proportional to x². This can be written as:
A ∝ x²
To remove the proportionality symbol and introduce a constant of proportionality, we can write it as:
A = kx²
Here, k represents the constant of proportionality. To find the exact relationship between the area and the side length, we need to determine the value of k. This can be done by considering a specific example.
Let's say we have a square with a side length of 5 units and an area of 25 square units. To find the value of k, we can substitute these values into our equation:
25 = k(5)²
25 = 25k
By dividing both sides of the equation by 25, we find that k = 1. Hence, the equation representing the relationship between the area and the side length is:
A = x²
Now, you can calculate the area of a square by squaring its side length. For example, if the side length is 8 units, you can find the area by calculating 8² = 64 square units.