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 be the perimeter,
be the length and
be the width:
.
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 centimeters and its width is
centimeters. What is its width?
Solution
A rectangle has two pairs of sides, so, just add the length and width twice. That is
.
So, the correct answer is .
Problem 2
The perimeter of a rectangle is centimeters. It’s width is
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 cm which sums up to
centimeters. We subtract
from
and the difference is
. Now, the two sides will share
centimeters equally, so each side is
centimeters. The longer side which is asked by the question is
centimeters.
Problem 3
The with of a rectangular garden is meters less than its length. Its perimeter is
meters. What are the dimensions of the garden?
Solution
Let be the length and
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
Simplifying the right hand sides, we have
Adding to both sides gives us
Dividing both sides by gives us
So, length is cm and width is
cm.
Problem 4
The perimeter of a rectangle is centimeters. It’s length is twice its width. What are the dimensions of the rectangle?
Solution
Let be the width of the rectangle and
be its length.
Perimeter = length + length + width + width
Adding the right hand side, we have
Diving both sides by results to
.
So, the width of the rectangle is and its length is
centimeters. So the garden is
meter.
The checking of the problems’ answers are left as an exercise.