How would I setup the equation for the perimeter and area of a similar (6inch width, and 8 inch length)rectangle that is increased by a ratio of 1:n?
perimeter= 6n*2 + 8n*2
so you know perimeter when n=1, and when n=n
Area= 6n*8n=48n^2
To set up the equation for the perimeter and area of a similar rectangle that is increased by a ratio of 1:n, you can follow these steps:
1. Determine the original dimensions of the rectangle. In this case, the original width is 6 inches and the original length is 8 inches.
2. Determine the ratio of increase, denoted by n. This ratio represents how much larger the new rectangle will be compared to the original. For example, if n=2, the new rectangle will be twice as large as the original.
3. Calculate the new dimensions of the rectangle by multiplying the original dimensions by the ratio n. In this case, the new width will be 6n inches and the new length will be 8n inches.
4. Calculate the perimeter of the new rectangle. The perimeter is the sum of all the sides of the rectangle. Since a rectangle has two pairs of equal sides, the perimeter can be calculated using the formula: P = 2(length + width). Substitute the new dimensions into the formula to get the new perimeter.
New Perimeter = 2(8n + 6n) = 2(14n) = 28n
Therefore, the equation for the perimeter of the new rectangle is P = 28n.
5. Calculate the area of the new rectangle. The area is the product of the length and width of the rectangle. Substitute the new dimensions into the formula to get the new area.
New Area = 8n * 6n = 48n^2
Therefore, the equation for the area of the new rectangle is A = 48n^2.
By following these steps, you can set up the equations for the perimeter and area of a similar rectangle that is increased by a ratio of 1:n.