Equation to find the perimeter of a rectangle

The perimeter is the length of the outline of a shape. To find the perimeter of a rectangle or square you have to add the lengths of all the four sides. x is in this case the length of the rectangle while y is the width of the rectangle.

The perimeter, P, is:

$$P= x+x+y+y$$

$$P=2x+2y$$

$$P=2(x+y)$$

Equation to find the perimeter of a rectangle


Example

Find the perimeter of this rectangle:

Equation to find the perimeter of a rectangle

$$P=7+7+4+4$$

$$P=2\cdot 7+2\cdot 4$$

$$P=2\cdot (7+4)$$

$$P=2\cdot 11$$

$$P=22\,in$$


The area is measurement of the surface of a shape. To find the area of a rectangle or a square you need to multiply the length and the width of a rectangle or a square.

Equation to find the perimeter of a rectangle

Area, A, is x times y.

$$A=x\cdot y$$


Example

Find the area of this square.

Equation to find the perimeter of a rectangle

$$A=x\cdot y$$

$$A=5\cdot 5$$

$$A=25\,in^{2}$$


There are different units for perimeter and area The perimeter has the same units as the length of the sides of rectangle or square whereas the area's unit is squared.


Video lesson

Calculate the perimeter and the area in feet

Equation to find the perimeter of a rectangle

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In rectangle, the distance around the outside of the rectangle is known as perimeter. A rectangle is 2-dimensional; however, perimeter is 1-dimensional and is measured in linear units such as feet or meter etc.

The perimeter of a rectangle is the total length of all the four sides.
Perimeter of rectangle = 2L + 2W.

Example 1: Rectangle has the length 13 cm and width 8 cm. solve for perimeter of rectangle.

Solution:
Given that:

Length (l) = 13 cm
Width (w) = 8 cm

Perimeter of the rectangle = 2(l + w) units
P = 2(13 + 8)
P = 2 (21)
P = 42

Thus, the perimeter of the rectangle is 42 cm.

Example 2: If a rectangle's length is 2x + 1 and its width is 2x – 1. If its area is 15 cm2, what are the rectangle's dimensions and what is its perimeter?

Solution:
We know that the dimensions of the rectangle in terms of x:

 l = 2x + 1
w = 2x – 1

Since the area of a rectangle is given by:
A = l * w

We can substitute the expressions for length and width into the equation for area in order to determine the value of x.

A = l * w
15 = (2x + 1) (2x -1)
15 = 4x2 – 1
16 = 4x2
x = ±2
 
 Note that the value of x must be positive and therefore in our case, the value of x is 2. And now we have:

l = 5 cm
w = 3 cm
Therefore, the dimensions are 5cm and 3cm.

Now, substituting these values in the formula for perimeter, we will get


P = 2l + 2w
P = 2(5)+2(3)
P = 10+6
P = 16 cm

Example 3: Find the area and the perimeter of a rectangle whose length is 24 m and width is 12m?

Solution:
Given that:

length = L = 24m
width = W = 12m

Area of a rectangle:
A = L × W
A = 24 × 12
A = 188 m2

Perimeter of a rectangle:
P = 2L + 2W
P = 2(24) + 2(12)
P = 48 + 24
P = 72 m

Example 4: Find the area and perimeter of a rectangle whose breadth is 4 cm and the height 3 cm.

Solution:
Area = b×h = 4×3 = 12 cm2.
Perimeter = 2(b) + 2(h) = 2(4) + 2(3) = 8 + 6 = 14.

Example 5: Calculate the perimeter of the rectangle whose length is 18cm and breadth 7cm

Solution:
Given that:

L = 18 cm
B = 7 cm

Perimeter of rectangle = 2(length + breadth)
P = 2 (L + B)
P = 2 (18 + 7)
P = 50 cm

Example 6: Find the perimeter of rectangle whose length is 6 inches and width is 4 inches.

Solution:
P = 2(L + B)
P = 2(6 + 4)
P = 20 in

Example 7: A boy walks 5 times around a park. If the size of the park is 100m by 50m, find the distance the boy has walked. If he walks 100m in 5 minutes, how long will it take for him in total?

Solution:
Given that:
Length = L = 100m
Width = W = 50m
Rounds = 5
Time per 100m = 5minutes.

Perimeter of the park:
P = 2 L + 2 W.
P = 2 × 100 + 2 × 50
P = 200 + 100
P = 300 m

Total distance walked = 5 × Perimeter of the park.
= 5 × 300
= 1500 meters

Total time taken = Total distance walked × time taken to walk 1m.
= 1500 × 5/100
= 75minutes or 1hr 15minutes

Online Perimeter Calculator

What are the units of the 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?

How do you find the perimeter of a word?

The key to solving perimeter word problems is to know two things: 1) The formula of the perimeter of a rectangle. Perimeter of a Rectangle Formula: { extbf { extit {P = 2L + 2W}}} Remember that the length (L) is the longest side of the rectangle while the width (W) is the shortest side.

What is the formula to find the width of a rectangle?

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.

How do you find the perimeter of a 4 sided polygon?

A four-sided polygon having two dimensions i.e. length and breadth is called a rectangle. To calculate the perimeter of the rectangle we have to add all the four sides of the rectangle. In a rectangle, the opposite sides of a rectangle are equal and so, the perimeter will be twice the width of the rectangle plus twice the height of the rectangle.

What is the formula for finding the perimeter of a rectangle?

Perimeter of Rectangle = 2 (Length + Width). Rearranging the terms in this formula, we get, Length = P e r i m e t e r 2 – Width. So, to find the length of a rectangle, subtract the width from half of the perimeter.

What is the equation for perimeter?

In order to find the perimeter, or distance around the rectangle, we need to add up all four side lengths. This can be done efficiently by simply adding the length and the width, and then multiplying this sum by two since there are two of each side length. Perimeter=(length+width)×2 is the formula for perimeter.

What are the 3 formulas for perimeter?

The formula to calculate the perimeter of a square can be given as,.
Perimeter of a Square, (P) = 4 × Side units..
Perimeter of a Rectangle, (P) = 2(l + b) units..
Perimeter of a Triangle = Sum of all three sides..
Perimeter of a Circle = 2 π r = π d..