A rectangle has an area of 18 m2. Find a function that models its perimeter P in terms of the length x of one of its sides.
2 x + 2 y = P
y = 18/x
2x + 36/x = P
Why did the rectangle enroll in a math class? Because it wanted to find the formula for its own perimeter! So, let's solve this puzzle together.
We know that the area of a rectangle is given by the formula A = length * width. In this case, we have the area A = 18 m^2. Since we are only given one side x, let's assume that it represents the length. We can write the equation as 18 = x * width.
Now, the perimeter of a rectangle is given by the formula P = 2 * (length + width). We want to find a function that models the perimeter P in terms of the length x. So, let's substitute the width with our expression 18/x, giving us P = 2 * (x + (18/x)).
And voila! We've found our function! P(x) = 2 * (x + (18/x)). Now go ahead and plug in the value of x, and you'll get the perimeter of the rectangle. Just remember to bring a bit of circus music along, just in case!
To find a function that models the perimeter P of a rectangle in terms of the length x of one of its sides, we need to know the formula for the area of a rectangle and the formula for the perimeter of a rectangle.
The formula for the area of a rectangle is given by A = length * width, and in this case, we know that the area of the rectangle is 18 m^2.
So, we can write the equation as A = x * width = 18.
The formula for the perimeter of a rectangle is given by P = 2 * (length + width).
Let's denote the width of the rectangle as y.
So, the perimeter can be written as P = 2 * (x + y).
From the equation A = x * y = 18, we can solve for y:
y = 18 / x.
Substituting this value of y into the equation for perimeter P, we get:
P = 2 * (x + (18 / x)).
Thus, the function that models the perimeter P in terms of the length x of one of its sides is:
P(x) = 2 * (x + (18 / x)).
To find a function that models the perimeter P of a rectangle in terms of the length x of one of its sides, we first need to understand the relationship between the length and the perimeter.
The perimeter of a rectangle is the sum of all four sides. In this case, since the length of one side is x, the other side will also be x, and the remaining two sides will be the width of the rectangle.
Let's denote the width of the rectangle as y.
From the given information, we know that the area of the rectangle is 18m². The area of a rectangle is found by multiplying the length and width together, so we have the equation:
Area = length * width
18 = x * y
To find a function that models the perimeter in terms of the length, we need to express the perimeter in terms of x and y.
The perimeter P can be calculated by adding all four sides:
P = 2 * length + 2 * width
P = 2x + 2y
Since we have an equation for the area in terms of x and y, we can try to rearrange it to solve for y:
18 = x * y
y = 18 / x
Now we can substitute the value of y into the equation for the perimeter:
P = 2x + 2(18 / x)
P = 2x + 36 / x
Therefore, the function that models the perimeter P in terms of the length x of one of its sides is:
P(x) = 2x + 36/x