## 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)

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

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