Perimeter of a Rectangle
Rectangles are foursided polygons. Following are the properties of a rectangle:
(i) All the angles of a rectangle are 90º.
(ii) Opposite sides of a rectangle are always the same in size.
Perimeter of a rectangle
The perimeter of a rectangle is the total length of all the sides of the rectangle. Hence, we can find the perimeter by adding all four sides of a rectangle.
Perimeter of the given rectangle is a + b + a + b. Since opposite sides of a rectangle are always equal, we need to find the dimensions of only two sides to find the perimeter of a rectangle.
The perimeter of the above rectangle with sides ‘a units’ and ‘b units’ is:
a + b + a + b = 2a + 2b = 2 (a + b) units.
Hence, the formula for the perimeter of a rectangle = 2 × (sum of adjacent sides)
Examples of finding the perimeter of a rectangle
Example 1. The two sides of the rectangle are given. What will be the perimeter of the rectangle?
Solution: One side of the rectangle is 2 cm and the other side is 5 cm.
We know that, the perimeter of a rectangle = 2 × (sum of adjacent sides)
Therefore, the perimeter of the rectangle = 2 × (5 + 2) = 2 × (7) = 14 cm
Example 2. A rectangular playground is 20 m long and 13 m wide. Find its perimeter.
Solution: One side of the rectangular playground is 20 m and the other side is 13 m.
We know that, the perimeter of a rectangle = 2 × (sum of adjacent sides)
Therefore, the perimeter of the rectangular ground = 2 × (20 + 13) = 2 × (33) = 66 m
Tricky problems involving perimeter of rectangles
Type I: When the perimeter and only one of the sides are given.
Example 1. If the perimeter of the given rectangle is 10 cm and the length of one of its sides is 2 cm. What will be the other side?
Solution: The perimeter of the rectangle, with one of the sides equal to 2 cm, is 10 cm.
Let the missing side be ‘a’.
We know that, the perimeter of a rectangle = 2 × (sum of adjacent sides)
10 = 2 × (2 + a) 5 = (2 + a)
a = 5  2 = 3 cm
Type II: Finding sides using the properties of a rectangle.
Example 2. In the given rectangle, if a = 4 cm and d = 3 cm. Find b and c.
Solution: We know that side a = 4 cm and side d = 3 cm.
To find side b and c, we use the property that the opposite sides of a rectangle are always the same in size.
Hence, a = c = 4 cm and d = b = 3 cm.
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