Perimeter of a rectangle


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:

Example 1:

Find the perimeter of a rectangle in which the length of the rectangle is 10 cms and breadth is half the length.

Answer:

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.

Example 2:

Find the perimeter of a rectangle whose area is 22 sq. cms and in which the length of a diagonal is 10 cms.

Answer:

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.

Perimeter worksheets



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