how to find the length and width of a rectangle when given the perimeter

Perimeter of Rectangle

The perimeter of rectangle is the total distance of its outer boundary. It is twice the sum of its length and width and it is calculated with the help of the formula: Perimeter = 2(length + width).

1.	What is the Perimeter of a Rectangle?
2.	Perimeter of Rectangle Formula
3.	How to Find the Perimeter of Rectangle?
4.	Usage of Perimeter of a Rectangle
5.	Perimeter of a Rectangle Calculator
6.	FAQs on Perimeter of a Rectangle

What is the Perimeter of a Rectangle?

The perimeter of a rectangle is the total length or distance of its boundary on all sides. The perimeter of a rectangle is a linear measure and has the same linear units of meters, feet, inches, or yards. Let us first understand the two main properties of a rectangle.

All four angles of a rectangle are 90°.
The opposite sides of a rectangle are equal in measure.

Imagine a rectangular park in your neighborhood. Have you ever thought about how long its boundary is?

Perimeter of a rectangle

If you go around the park along its boundary once, you cover a distance. This distance is the perimeter of the park. In order to measure the perimeter of any rectangular field, you travel along the boundary of the four sides of the field. You begin at a fixed point called the starting point and end when you reach the starting point again. This length or distance of the boundary is called the perimeter of a rectangle.

Perimeter of Rectangle Formula

The formula used to calculate the perimeter of a rectangle is, perimeter of a rectangle = 2(l + w) units, where 'l' is the length and 'w' is the width of the rectangle. Let us understand this with the help of a simple example. David wants to put a fence around his farm so that his sheep will not wander away. Let us now understand this formula with an example. He wants to know how much wire he would need to put a fence around his rectangular farm.

Perimeter of rectangular farm

Let us first name the sides of his farm. The larger side of this rectangular farm is named (l). The smaller side is named (w). Now, if we add the distance of all 4 sides of his farm, it will give us the perimeter. Total distance = l + w + l + w = 2l + 2w. Therefore, the Perimeter of the rectangle = 2(l + w).

How to Find the Perimeter of a Rectangle?

We can calculate the perimeter of a rectangle in three simple steps. The three steps listed below are helpful to find the perimeter.

Step 1: To calculate the perimeter of a rectangle, the length, and width should be known.
Step 2: The respective values of length and width are substituted in the formula.
Step 3: After solving the equation, the value of the perimeter is calculated.

The formula used to calculate the perimeter of a rectangle is:

Perimeter of a rectangle = 2(l + w).

Let us look at two different cases of the perimeter of a rectangle formula.

If the perimeter and the length of a rectangle are known, the width can be calculated using the formula: Width = P/2 - l, where l = length of the rectangle; and w = width of the rectangle, and P = perimeter of the rectangle.
In the same way, if the perimeter and the width are known, the length can be calculated using the formula: Length(L) = P/2 - w. Where P = perimeter of the rectangle; and w = width of the rectangle.

Usage of Perimeter of a Rectangle

The Perimeter of a rectangle makes things easier and helps us in calculating distances and lengths in our day-to-day lives.

For example,

If you need to decorate the border of your rectangular notebook, you can easily calculate how much ribbon you would need by finding the perimeter.
If you need to put a fence around your garden, the perimeter of the garden will give you the exact length of wire you would need.

Can you think of other similar examples related to the perimeter of a rectangle?

Perimeter of a Rectangle Calculator

Try now Cuemath's 'Perimeter of a rectangle Calculator', an online tool that calculates the perimeter of a rectangle. It is the easiest and the fastest method for kids to calculate the answers promptly in seconds.

☛ Related Articles

To enhance your calculations and in-depth understanding of the perimeter of a rectangle check out few more interesting articles listed below.

Area and Perimeter Of Rectangles Worksheets
Perimeter of Rectangle Worksheets

Perimeter of a Rectangle Examples

Example 1: Ann wants to add some lace as decoration to the borders of her bedsheet. The bedsheet is in the shape of a rectangle. The length of the bedsheet is 120 inches and the width is 85 inches. How much lace will she need to put around it?

Solution:

Given, length = 120 inches; width = 85 inches. We know that the perimeter of a rectangle is equal to twice the sum of its length and width. Hence, Perimeter of a rectangle = 2(l+w). Applying the values of length and width in this formula, we have Perimeter = 2(l + w) = 2(120 + 85)= 2 × 205 = 410 inches.

Therefore, Ann will need 410 inches of lace.
Example 2: Your favorite chocolate bar is made up of equal-sized squares with each side measuring 1 inch. Calculate the perimeter of the rectangular choco bar.

Solution:

We know that each little square has all its sides equal to 1 inch. If we count and add the sides of the squares along the length of the bar, we get 6 inches. The sides of squares along the width of the bar add up to 2 inches. Therefore, the length of the bar is 6 inches and the width of the bar is 2 inches. Applying this in the perimeter formula we have:

Perimeter = 2(l+w)= 2 (6+2) = 2×8 = 16 inches

Therefore, the perimeter is 16 inches.

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Practice Questions on Perimeter of a Rectangle

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FAQs on Perimeter of a Rectangle

What is Perimeter of Rectangle in Math?

The perimeter of a rectangle in math is a measurement value that is defined as the total length or distance around the boundaries of a rectangular shape. The perimeter of a rectangle is measure in meters, feet, inches, or yards.

What is the Perimeter of a Rectangle Formulas?

Formulas used to calculate the perimeter of a rectangle are:

Perimeter of a rectangle = 2(l + w).
If the perimeter and the length of a rectangle are known, the width = P/2 - l, where l = length, w = width, and P = perimeter of the rectangle.
If the perimeter and the width are known, Length(L) = P/2 - w. Where P = perimeter of the rectangle; and w = width.

☛ Check all the important maths formulas:

Perimeter Formula
Measurement Formula
Geometry Formulas

How to Find the Area of a Rectangle in Terms of Perimeter of a Rectangle?

If the perimeter of a rectangle is given, we also need to know either the length or the width to find its area. For example, if the length and perimeter is given, the width can be calculated. Perimeter = 2(length + width), width = (Perimeter/2) - length. Now, the required values to find the area of a rectangle are known. So, these values can be substituted in the formula: Area = length × width.

How to Find Perimeter of Rectangle with Diagonal?

If the diagonal of a rectangle is given then by using the following perimeter of rectangle formula we can determine the perimeter of a rectangle.
Perimeter of rectangle with diagonal = 2l + 2 \(\sqrt{d² - l²}\)Units.

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Diagonal of Square
Diagonals

How to Find the Perimeter of a Rectangle?

The perimeter of a rectangle is twice the sum of its length and width and it is calculated with the help of the formula: Perimeter = 2(length + width). It is the measure of the total boundary of the rectangle.

What are the Units of Perimeter of a Rectangle?

The units of the perimeter of a rectangle are the same as its length which is usually given in meters, centimeters, inches, or yards. The perimeter is equal to the boundary of the rectangle which can be calculated with the formula: Perimeter = Length + Length + Width + Width = 2(Length + Width).

Is the Area and Perimeter of a Rectangle the Same?

No, the area and the perimeter of a rectangle are different. The area of a rectangle is the total space covered by it and it is expressed in square units, while the perimeter is the total measure of its boundary and it is expressed in linear units.

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Perimeter
Area

What is the Perimeter of a Rectangle with the Area Given?

If the area of a rectangle is given, we need to know either the length or the width of the rectangle to find its perimeter. For example, if the length and the area is known, the width can be calculated: Area = length × width. So, width = Area /length. Now, all the required values to calculate the perimeter of a rectangle are known. So, these values can be substituted in the formula: Perimeter = 2(length + width).