Perimeter of a Rectangle:

A perimeter is defined as the length of an outline of a shape. In a circle, it refers to the circumference. To identify a rectangle or square’s perimeter, all you need to do is simply add the lengths of all four sides of a rectangle or a square. 

Suppose, if “a” is the rectangle length while “b’ is the rectangle width. Then in such a case, the perimeter is found by adding all four sides as given below:

P=a+a+b+b

P=2a+2b

P=2a+2b

P=2(a+b)

How to find the length of a side when perimeter and breadth are given?

 If “P” is the perimeter, and ‘a’ and ‘b’ are length and breadth respectively. Then,

Length of the rectangle (a) = (P/2) - b 

Similarly, breadth “b” can be found if perimeter “P” and length “l” are given.

Breadth (b) of the rectangle (a) = (P/2) - a 

Area of rectangle:

Consider a rectangle with a length of 'a' units and a width of 'b' units.

Hence, the rectangle's area is given by: 

Area (rectangle) = length × breadth

Therefore, A = a × b square units.

How to find the length of a side when an area and breadth are given?

 If “A” is the area, and ‘a’ and ‘b’ are length and breadth respectively. Then,

Length (a) = Area (A)/ Breadth (b).

Similarly, breadth “b” can be found if area “A” and length “l” are given.

Breadth (b) = Area (A)/Length (a)

Diagonal of the rectangle: The diagonal of a rectangle follows the Pythagoras theorem. That is, the diagonal is equal to the sum of squares of the remaining two sides. If a and b are sides of a rectangle, then diagonal (d) = a^2 + b^2. Here, the “^” symbol refers to power. 

Problems

Q1) Find the perimeter of the rectangle if the length and breadth are 7 and 2 respectively.

Answer 1) Initially, let us draw a diagram of a rectangle with length and breadth as 7 and 2 respectively.

Perimeter = 2(l + b)

P = 2(7+2)

P = 2 x 9 = 18 m

Q2) Find the length of the rectangle if the perimeter and breadth are 18 and 2 respectively.

Answer 1) Initially, let us draw a diagram of a rectangle with length and breadth as 7 and 2 respectively.

If “P” is the perimeter, and “x” and b are length and breadth respectively. Here “x” is an unknown quantity. Then,

Length of the rectangle (x) = (P/2) - b 

Therefore length of the rectangle = (18/2) - 2 = 9 - 2 = 7 m 

Q3) Find the area of the rectangle if the length and breadth are 7 and 2 respectively.

Answer 3) The formula for area of a rectangle is given by:

Area (rectangle) = length × breadth

Here length = 7 and breath = 2

Therefore, Area of rectangle = 7 m x 2 m = 14 m^2 (or 14 meter square)