A rectangle has an area of 15 m2. Find a function that models its perimeter P in terms of the length x of one of its sides.
Why did the rectangle go to the doctor? Because it was feeling a little un-square!
Now, to find a function that models the perimeter of the rectangle in terms of the length of one of its sides, let's call the length x and the width y. We know that the area of the rectangle is given by xy, and in this case, it's 15 m^2. So we can write one equation as xy = 15.
The formula for the perimeter of a rectangle is P = 2(x + y). Since we want to express it in terms of only one side, we can rewrite it as P = 2(x + 15/x).
So the function that models the perimeter P in terms of the length x of one of its sides is P(x) = 2(x + 15/x).
To find a function that models the perimeter P in terms of the length x of one of the sides, we need to first determine the relationship between the perimeter and the length of the sides.
In a rectangle, there are two pairs of equal sides. Let's say the length of one side is x. Then, the adjacent side also has length x. The other two sides will have different lengths, but they will be equal to each other. Let's call the length of these two sides y.
The formula for the area of a rectangle is given by A = length × width. In this case, the area is given as 15 m², which gives us the equation 15 = x × y.
Now, let's calculate the perimeter of the rectangle. The perimeter is the sum of all four sides. In terms of the variables x and y, the perimeter P is given by P = 2x + 2y.
We want to express the perimeter P in terms of x alone. To do this, we need to eliminate the variable y from the equation above. From the equation 15 = x × y, we can solve for y: y = 15/x.
Plugging this expression for y into the equation for the perimeter, we have P = 2x + 2y = 2x + 2(15/x).
Simplifying further, we get P = 2x + 30/x.
Thus, the function that models the perimeter P in terms of the length x of one of the sides is:
P(x) = 2x + 30/x.
To find a function that models the perimeter of a rectangle in terms of the length of one of its sides, we need to consider that a rectangle has two pairs of equal sides. Let's assume that the length of one side of the rectangle is x, and let's call the other side y.
We know that the area of a rectangle is given by the formula: Area = length × width. In this case, the area is given as 15 m². Therefore, we have the equation:
15 = x * y.
Now, the perimeter of a rectangle is given by the formula: Perimeter = 2(length + width). In this case, the perimeter P would be:
P = 2(x + y).
Since we need to express P in terms of x, we need to find a way to eliminate y in the above equation using the information about the area.
We can rearrange the area equation to solve for y:
y = 15 / x.
Substituting this value of y in our perimeter equation, we get:
P = 2(x + 15 / x).
Hence, the function that models the perimeter P in terms of the length x of one of the sides is:
P(x) = 2(x + 15 / x).