## 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.

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.

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.