Perimeter of a rectangle
Finding the perimeter of a rectangle when the length and the width are given and finding the length or the width when the perimeter is given are the goals of this lesson
Given a rectangle with side length (l) and width (w), the perimeter (P) or distance around the outside of the rectangle can be found by doing
P = l + w + l + w = 2 × l + 2 × w
Example #1:
Find the perimeter of a rectangle when l = 5 cm and w = 3 cm
P = 2 × 5 + 2 × 3
P = 10 + 6
P = 16
Notice that it is perfectly ok to do P = 5 + 3 + 5 + 3 = 8 + 8 = 16
However, it is usually easier and quicker to multiply each dimenssion by 2 and adding the result.
Example #2:
Find the perimeter of a rectangle when l = 9 cm and w = 5 cm
P = 2 × 9 + 2 × 5
P = 18 + 10
P = 28
Example #3:
Find the perimeter of a rectangle when l = 2/4 cm and w = 3/6 cm
P = 2 × 2/4 + 2 × 3/6
P = 2/1 × 2/4 + 2/1 × 3/6
P = (2 × 2)/(1 × 4) + (2 × 3)/(1 × 6)
P = 4/4 + 6/6
P = 1 + 1 = 2 cm
Example #4:
A rectangle has a perimeter of 14 inches. Find the length of the rectangle if the width is 4 inches
Here, given the perimeter and the width, you are asked to find the length of the rectangle.
We know that P = 2 × l + 2 × w
You should replace P by 14 and w by 4 because that is what they gave you.
So, 14 = 2 × l + 2 × 4
14 = 2 × l + 8
The problem becomes a
two step equations that you need to solve
However, you can solve this equation with mental math. Just say to yourself, " 8 plus what equal 14? "
Since 8 + 6 = 14, 2 × l must equal 6
Ask yourself now, " 2 times what equal 6? "
Since 2 times 3 is 6, l = 3
Example #5:
A rectangle has a perimeter of 18 inches. Find the width of the rectangle if l is 5 inches
Here, given the perimeter and the length, you are asked to find the width of the rectangle.
We know that P = 2 × l + 2 × w
You should replace P by 18 and l by 5 because that is what they gave you.
So, 18 = 2 × 5 + 2 × w
18 = 10 + 2 × w
Again, the problem is a
two step equations that you need to solve
However, you can solve this equation with mental math. Just ask yourself, " 10 plus what equal 18? "
Since 10 + 8 = 18, 2 × w must equal 8
Ask yourself now, " 2 times what equal 8? "
Since 2 times 4 is 8, w = 4