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.