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.

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)

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

Workout Examples

Example 1: Find the perimeter of the given plane figure.

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

You can comment your questions or problems regarding the perimeter of rectangle here.