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Geometry
> Perimeter of a Rectangle
Perimeter of a Rectangle
In rectangle, the distance around the outside of the rectangle is known as perimeter. A rectangle is 2dimensional; however, perimeter is 1dimensional 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 cm
^{2}
, 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 = 4x
^{2}
– 1
16 = 4x
^{2}
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 m
^{2}
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 cm
^{2}
.
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
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