a Review the formula for the perimeter of a rectangle.
B
b How many variables does the formula for the perimeter of a square have?
C
c Review the formulas for the area and perimeter of a square.
A
a Yes. Substitute s for each of a and b to get the perimeter.
B
b No. We need to know the length and width of a rectangle to find its perimeter.
C
c A=P^2/16
Practice makes perfect
a Let's begin by reviewing the formula for the perimeter of a rectangle.
As we can see, to find the perimeter we multiply the base and the height by 2 and add the to each other. Now we can consider any square.
Notice that in this case the base and the height are of the same length, s. Therefore, we can substitute b=s and h=s in the formula for the perimeter of a rectangle.
P=2s+2s=4s
As we can see, it gives us the formula for the perimeter of a square! Therefore, we can use the formula for the perimeter of a rectangle to find the perimeter of any square.
b The formula for the perimeter of a square is written below. P=4s
Here s is the length of a side of a square. In a rectangle we have the base b and height h, which very often have different lengths. We use both of them to determine the area of a rectangle. Thus, we cannot use the formula for the perimeter of a square for a rectangle, as it has only one variable.
c Let's review the formulas for the perimeter and the area of a square with side length s.
Perimeter
Area
P=4s
A=s^2
Notice that we have s in both of them. We can isolate s from the formula for perimeter and substitute it in the formula for the area!
