Before we discuss and use the formula for perimeter of a rectangle, let us define a few terms, out of necessity.
A rectangle is a parallelogram in which the angles at the four vertices A, B, C and D are all equal, and each one measures 90 degrees.
A rectangle has two different dimensions. They are length and breadth.
The longer side, or dimension, is conventionally called the length; while, the shorter side, the breadth.
Length of a rectangle is normally denoted by the letter l; and
Breadth, by the letter, b.
Perimeter of a rectangle, or for that matter perimeter of any figure, is the sum of all of the surrounding sides.
In a rectangle, the surrounding sides are two sides of equal length and two other sides of equal width.
So, perimeter of a rectangle = 2l + 2b = 2(l + b)
Let us solve a few questions on perimeter of a rectangle:
Find the perimeter of a rectangle in which the length of the rectangle is 10 cms and breadth is half the length.
Length, l = 10 and Breadth = 10/2 = 5.
Substitute 10 and 5 in the formula for the perimeter of a rectangle: 2 (l + b).
So, the perimeter will be = 2 (10 + 5) = 2 × 15 = 30 cms.
Find the perimeter of a rectangle whose area is 22 sq. cms and in which the length of a diagonal is 10 cms.
Recall the algebraic identity:
(l + b) 2 = l2 + b2 + 2lb
Area of a rectangle = l × b = 22,
Length of a diagonal of a rectangle is √ (l2 + b2).
Now, √ (l2 + b2) = 10,
So, by squaring on both sides, we get
l2 + b2 = 100.
Substitute 22 in l × b, and 100 in l2 + b2, in the algebraic identity
(l + b) 2 = l2 + b2 + 2lb to find the perimeter of the rectangle:
(l + b) 2 = 100 + 2 × 22 = 100 + 44 = 144
Applying square roots on both sides,
l + b = √ 144 = 12.
Therefore, perimeter of the rectangle will be 2 × 12 = 24 cms.
Area of a rectangle.