How to Find the Perimeter of a Rectangle?

The perimeter \(P\) of a rectangle is given by the formula:

\(P = 2 \times L + 2 \times W\)

where \(L\) and \(W\) are the length and width, respectively, of the rectangle.

How to Find the Perimeter of a Rectangle? Examples with Solutions

  1. Example 1: Find the perimeter of a rectangle of length 20 meters and width 10 meters.

    ► View Step-by-Step Solution

    Both the length \(L\) and the width \(W\) have the same units. Substitute \(L\) and \(W\) by their values in the formula of the perimeter:
    \(P = 2L + 2W = 2 \times 20 + 2 \times 10 = 40 + 20 = 60\text{ meters}\).

  2. Example 2: The length of a rectangle is 12.5 meters and its width is 800 centimeters. Find the perimeter of the rectangle in centimeters.

    ► View Step-by-Step Solution

    Since we need to find the perimeter in centimeters, we first convert the length into centimeters:
    \(L = 12.5\text{ meters} = 12.5 \times 100 = 1250\text{ centimeters}\)
    The perimeter \(P\) of the rectangle is given by:
    \(P = 2 \times L + 2 \times W = 2 \times 1250 + 2 \times 800 = 2500 + 1600 = 4100\text{ centimeters}\).

  3. Example 3: The length of a rectangle is 240 meters and its width is the third of its length. Find the perimeter of this rectangle.

    ► View Step-by-Step Solution

    First, find the width \(W\) of the rectangle given its length \(L = 240\text{ meters}\):
    \(W = \left(\dfrac{1}{3}\right) \times L = \left(\dfrac{1}{3}\right) \times 240 = \dfrac{240}{3} = 80\text{ meters}\)
    The perimeter \(P\) of the rectangle is given by:
    \(P = 2 \times L + 2 \times W = 2 \times 240 + 2 \times 80 = 480 + 160 = 640\text{ meters}\).

  4. Example 4: The width of a rectangle is 1200 meters and its length is 500 meters longer than its width. Find the perimeter of this rectangle.

    ► View Step-by-Step Solution

    First, find the length \(L\) of the rectangle given its width \(W = 1200\text{ meters}\):
    \(L = 500 + W = 500 + 1200 = 1700\text{ meters}\)
    The perimeter \(P\) of the rectangle is calculated as follows:
    \(P = 2 \times L + 2 \times W = 2 \times 1700 + 2 \times 1200 = 3400 + 2400 = 5800\text{ meters}\).

  5. Example 5: A large rectangular field of length 500 meters and width 400 meters is to be enclosed along its perimeter by a fence. What is the total cost of the fence if the rate is $2 per meter?

    ► View Step-by-Step Solution

    Find the perimeter \(P\):
    \(P = 2L + 2W = 2 \times 500 + 2 \times 400 = 1000 + 800 = 1800\text{ meters}\)
    Every meter costs \( \$2 \) to fence. Hence, the total cost \(C\) to fence this field is given by:
    \(C = P \times 2 = 1800 \times 2 = \$3600\).

More References and Links