The area of a rectangle is 25cm^2. Express the perimter of the rectangle in terms of its width.
A = Lw
25 = Lw
w = 25/L
P = 2w + 2L
P = 2(25/L) + 2L
P = 50/L + 2L
Let's assume that the width of the rectangle is denoted by "w" (in cm) and the length of the rectangle is denoted by "l" (in cm).
We know that the area of a rectangle is given by the formula:
Area = length × width.
In this case, we are given that the area is 25cm^2. So, we can write the equation as:
25 = l × w.
To express the perimeter of the rectangle in terms of its width, we need to find the relationship between the perimeter and the width of the rectangle.
The perimeter of a rectangle is given by the formula:
Perimeter = 2(length + width).
We can rewrite this formula in terms of the width as follows:
Perimeter = 2(w + length).
To proceed, we need to find the length of the rectangle in terms of its width. We can do this by rearranging the equation for the area:
25 = l × w
=> l = 25/w.
Substituting this value of "l" into the expression for the perimeter, we get:
Perimeter = 2(w + (25/w)).
Hence, the perimeter of the rectangle in terms of its width is given by the equation:
Perimeter = 2(w + (25/w)).
To express the perimeter of a rectangle in terms of its width, we need to know the length of the rectangle as well. However, in the given question, only the area of the rectangle is provided, and the length is not known.
To find the perimeter of the rectangle, we need to know both the length and the width.
Here's how you can find the perimeter when the area is given:
Step 1: Write down the formula for the area of a rectangle:
Area = Length x Width
Step 2: Substitute the given area into the formula:
25cm^2 = Length x Width
Step 3: Since the length is not known, we cannot directly express the perimeter in terms of the width. However, we can explore some possibilities based on the given area.
For example:
- If the width is 1cm, then the length would be 25cm.
- If the width is 5cm, then the length would be 5cm.
Step 4: Once you know the width and length of the rectangle, you can calculate the perimeter using the formula:
Perimeter = 2 x (Length + Width)
So, for the given area of 25cm^2, you can express the perimeter in terms of the width by calculating the perimeter using different possible values for the width and finding the corresponding length.