A square is a four-sided closed figure where the lengths of all the four sides will be equal and each vertex angle will be right angle or 90^{o }as shown below.
Let s be the length of each side of a square.
Then,
Perimeter = 4s
Example 1 :
Find the perimeter of the square having side length 14 cm.
Solution :
Formula for perimeter of a square :
= 4s^{ }
Substitute 14 for s.
= 4(14)
= 56
So, the perimeter of the square is 56 cm.
Example 2 :
If the perimeter of square is 32 inches, then find the length of each side.
Solution :
Perimeter of the square = 32 inches
4s = 32
Divide each side by 4.
s = 8
So, the length of each side of the square is 8 inches.
Example 3 :
The square has side length 250 cm. Find its perimeter in meter.
Solution :
Formula for perimeter of a square :
= 4s^{ }
Substitute 250 for s.
= 4(250)
= 1000 cm -----(1)
We know
100 cm = 1 m
Therefore, to convert centimeter to meter, we have to divide by 100.
(1)-----> Perimeter = 1000 cm
Divide the right side by 100 to convert cm into m.
Perimeter = (1000 / 100) m
= 10 m
So, the perimeter of the square is 10 meters.
Example 4 :
If the length of each diagonal of a square is 2√2 cm, then find its perimeter.
Solution :
To find the perimeter of a square, first we have to know the length of each side.
Let s be the length of each side of the square.
Draw a sketch.
In the figure shown above, consider the right triangle ABC.
By Pythagorean Theorem, we have
AB^{2} + BC^{2} = AC^{2}
Substitute.
s^{2} + s^{2} = (2√2)^{2}
Simplify and solve for s.
2s^{2} = 2^{2} ⋅(√2)^{2}
2s^{2} = 4 ⋅(2)
2s^{2} = 8
Divide each side by 2.
s^{2} = 4
Find positive square root on both sides.
√s^{2} = √4
√s^{2} = √(2 ⋅ 2)
s = 2
Formula for perimeter of a square.
Perimeter = 4s
Substitute 2 for s.
= 4(2)
= 8
So, the perimeter of the square is 8 cm.
Example 5 :
If the lengths of the sides of two squares are in the ratio 2 : 5. then find the ratio of their perimeters.
Solution :
From the ratio 2 : 5, let the sides of two squares be 2x and 5x respectively.
Formula for perimeter of a square :
= 4s
Perimeter of 1^{st} square = 4(2x) = 8x |
Perimeter of 1^{st} square = 4(5x) = 10x |
Ratio of the perimeters :
= 8x : 10x
Divide each term by 2x.
= 2 : 5
So, the ratio of the perimeters of two squares is 2 : 5.
Note :
The ratio of the sides of two squares and the ratio of the perimeters of two squares are same.
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