Perimeter of Rectangle

Perimeter of Rectangle

Perimeter of Rectangle

Total covering or outer length of a closed plane figure is called the perimeter of the figure. Rectangle is a quadrilateral or a four sided plane figure having its opposite sides equal and each angle 90°. Therefore the sum of the lengths of all four sides of a rectangle is the perimeter of rectangle.
rectangle ABCD of length l and breadth b
In a rectangle, the longer side is taken as length (l) and the shorter side is taken as breadth (b). In the given figure; ABCD is a rectangle, in which AB and CD are opposite sides and so are AD and BC.
                                Length of the rectangle ABCD = BC = AD = l
                                Breadth of the rectangle ABCD = AB = CD = b
                                Perimeter of the rectangle ABCD = BC + CD + AD + AB
                                                                                      = l +b +l +b
                                                                                      = 2l + 2b
                                                                                      = 2(l + b)
Hence the perimeter of the rectangle is given by the formula:
Perimeter = 2(l + b)

Also, the length of diagonal of the rectangle is given by
length of diagonal of the rectangle ABCD



Workout Examples

Example 1: Find the perimeter of the given plane figure.
rectangle ABCD of length 8 cm and diagonal 10 cm
Solution: Here,
                                ABCD is a rectange,
                                Length of diagonal AC (d) = 10cm
                                Length of rectangle (l) = 8cm
                                Breadth of rectangle (b) = ?
                                Perimeter (P) = ?
                                We have,
                                                d2 = l2 + b2
                                or,          (10cm)2 = (8cm)2 + b2
                                or,          100cm2 – 64cm2 = b2
                                or,          36cm2 = b2
                                             b = 6cm
                                Again,
                                Perimeter of rectangle (P) = 2(l + b)
                                                                             = 2(8cm + 6cm)
                                                                             = 2 × 14cm
                                                                             = 28cm
Example 2: Find the length of a wire to surround 5 times a rectangular ground with 10m length and 5m breadth.
Solution: Here,
                                Length of rectangular ground (l) = 10m
                                Breadth of rectangular ground (b) = 8m
                                 Perimeter of rectangular ground = 2(l + b)
                                                                                             = 2 (10 + 8)m
                                                                                             = 2 × 18m
                                                                                             = 36m
                                 The length of wire to surround 5 times = 5 × 36m
                                                                                                       = 180m.
Example 3: The length of a rectangular ground is three times of its breadth. If its perimeter is 24m, find its length and breadth.
Solution: Let,
                                Breadth of rectangular ground (b) = x m
                                  Length of rectangular ground (l) = 3x m

                                 Perimeter of the ground = 24m
i.e.          2(l + b) = 24
or,          2(3x + x) = 24
or,          2 × 4x = 24
or,          8x = 24
or,          x = 24/8
or,          x = 3m
                                  Length of rectangular ground (l) = 3x = 3 × 3 = 9m
          Breadth of rectangular ground (b) = x = 3m


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