How to Solve Perimeter of Rectangle Word Problems

The perimeter of a polygon is the sum of all the lengths of its sides. Since a rectangle has two pairs of sides, if we call the longer side length and the shorter side width, then

Perimeter = length + length + width + width.

We can shorten this formula if we let P be the perimeter, l be the length and w be the width:

P = l + l + w + w

P = 2l + 2w.

You see, you don’t have to memorize the formula as long as you know the concept and you know the shape of the polygon. In some of the examples, below, I did not show use the shorter formula since they can be solved intuitively.

Problem 1

The length of a rectangle is 12 centimeters and its width is 13 centimeters. What is its width?

Solution

A rectangle has two pairs of sides, so, just add the length and width twice. That is

12 + 12 + 13 + 13 = 50.

So, the correct answer is 50 cm.

Problem 2

The perimeter of a rectangle is 36 centimeters. It’s width is 8 centimeters. What is its length?

Solution

As much as possible, train yourself to solve problems intuitively. This problem for example does not need to use Algebra. Just draw the triangle and then label appropriately.

perimeter of rectangle

The two shorter sides are 8 cm which sums up to 16 centimeters. We subtract 16 from 36 and the difference is 20. Now, the two sides will share 20 centimeters equally, so each side is 10 centimeters. The longer side which is asked by the question is 10 centimeters.

Problem 3

The with of a rectangular garden is 3 meters less than its length. Its perimeter is 42 meters. What are the dimensions of the garden?

Solution

Let x be the length and x - 3 be the width of the rectangle.

Screen Shot 2014-03-23 at 7.49.41 PM

Now, we know that the perimeter of a rectangle is described by the equation

Perimeter = length + length + width + width

Substituting, we have

42 = x + x + (x - 3) + (x - 3)

Simplifying the right hand sides, we have

42 = 4x - 6

Adding 6 to both sides gives us

48 = 4x

Dividing both sides by 4 gives us

12 = x

So, length is 12 cm and width is 12 - 3 = 9 cm.

Problem 4

The perimeter of a rectangle is 48 centimeters. It’s length is twice its width. What are the dimensions of the rectangle?

Solution

Let x be the width of the rectangle and 2x be its length.

Perimeter = length + length + width + width

48 = 2x + 2x + x + x

Adding the right hand side, we have

48 = 6x

Diving both sides by 6 results to

8 = x.

So, the width of the rectangle is 8 and its length is 2(8) = 16) centimeters. So the garden is 8 \times 16 meter.

The checking of the problems’ answers are left as an exercise.

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