What is the perimeter of a 2 inch square if the length of each side is doubled?
Square is a two-dimensional figure characterized by four sides, preferably, denoted as edges and its intersection points known as the vertices respectively. All four sides of the square are equal in length. It is a special case of a rectangle where all the sides are equal
Properties of a square
Some of the properties of a square are as follows :
- All four sides of the square are equal to each other.
- The opposite sides of a square are parallel to each other.
- All angles of the square measure 90°.
- The sum of all interior angles is 360°.
- Length of diagonals is equal.
- The length of the diagonal with sides s is √2 × s
- Since the sides of a square are parallel, it is also called a parallelogram.
Perimeter of a square
Perimeter of a square = Sum of all four sides
Therefore,
Let us assume the side of the square to be x.
Now,
Since all the four sides of the square are equal in length, we have,
Perimeter of a square = x + x + x + x
= 4x
What is the perimeter of a 2 inch square if the length of each side is doubled?
Solution:
Originally, we have,
Side of a square, s = 2 inch
Perimeter of the square, P = 4 * side of the square
= 4 * s inch
= 4 * 2 inch
= 8 inch
Thus, P = 8 inches
Now, we have,
Side of the square is doubled.
Therefore,
Side of a square, s’ = 2 * 2 inch
= 4 inch
Perimeter of the square, P’ = 4 * side of the square
= 4 * s’ inch
= 4 * 4 inch
= 16 inch
P’ = 16 inches
Thus, the perimeter becomes two times, when each side is doubled.
Sample Questions
Question 1. Assume that the side of a square is 40 inches if the sides of the square are tripled, Then calculate how many times the new perimeter of the square becomes?
Solution:
Here we have to find how many times the perimeter will be increased if the side of the square is tripled
As we know that
Perimeter of a square = 4 × side
Given: Side of the square is 40 inch
Perimeter of a square = 4 × 40
Perimeter of a square = 160 inch
Further,
When the side of the square is tripled
Side of the new square = 3 × 40
Side of the new square = 120 inch
Now,
Perimeter of the new square = 4 × side
Perimeter of the new square = 4 × 120
Perimeter of the new square = 480 inch
Further,
To find how many times the perimeter is increased
Increase in the perimeter =
Increase in the perimeter =
Increase in the perimeter = 3 times
Therefore,
We can see that the perimeter of the new square is triple the perimeter of the original square
Thus,
The perimeter of a square is increased by 3 times when its sides are tripled.
Question 2. Calculate how many times the perimeter of a square will be reduced if the side of a square is reduced to half. Given that the side of the original square is 25 inches?
Solution:
Here we have to find how many times the perimeter will be reduced if the side of the square is halved.
As we know that
Perimeter of a square = 4 × side
Given: Side of the square is 25 inch
Perimeter of a square = 4 × 25
Perimeter of a square = 100 inch
Further,
When the side of the square is halved
Side of the new square =
Side of the new square = 12.5 inch
Now,
Perimeter of the new square = 4 × side
Perimeter of the new square = 4 × 12.5
Perimeter of the new square = 50 inch
To find how many times the perimeter is decreased
Decrease in the perimeter =
Decrease in the perimeter =
Decrease in the perimeter = 2 times
Therefore,
We can see that the perimeter of the new square is reduced by 2 times the perimeter of the original square
Thus,
The perimeter of a square is reduced to half when its sides are halved.
Question 3. Assume that the perimeter of a square is increased by four times, So find how many times the new side of the square becomes. It is given that the perimeter of the original square is 120 feet?
Solution:
Here we have to find the increase in the side of the square when its perimeter is increased by four times
As we know that
Perimeter of a square = 4 × side
Given: Perimeter of the original square is 120 feet
Perimeter of the original square = 120 feet
Perimeter of the original square = 4 × side
120 = 4 × side
Side =
Side of the original square = 30 feet
Further,
Perimeter of the original square is increased by four times
Perimeter of the new square = 4 × 120
Perimeter of the new square = 480 feet
Perimeter of the new square = 4 × side
480 = 4 × side
Side =
Side = 120 feet
Side of the new square = 120 feet
Now,
Side of the original square = 30 feet
Side of the new square = 120 feet
To find how many times the side is increased
Increase in the side =
Increase in the perimeter =
Increase in the perimeter = 4 times
Therefore,
We can see that the side of the new square is increased by four times the side of the original square
Thus,
The side of a square is increased by four times when its perimeter is increased by four times.
Question 4. Calculate the perimeter of the square if the area of the square is 64 inch2?
Solution:
Here we have to find the perimeter of the square by the given area.
Given: Area of the square is 64 inch2.
As we know that
Area of the square = Side × Side
Area of the square = s × s
64 = s × s
s2 = 64
s =
s = 8 inch
Side of the square is 8 inch
Further,
Perimeter of the square = 4 × side
Perimeter of the square = 4 × 8
Perimeter of the square = 32 inch
Therefore,
Perimeter of the square is 32 inch.
Question 5. Assume that the side of a square is increased by 8 times, so calculate by how many times the area of the new square will become. Given that the side of the original square is 20 inches.
Solution:
Here we have to find how many times the area will be increased if the side of the square is increased by 8 times.
As we know that
Area of a square = side × side
Given: Side of the square is 20 inch
Area of a square = 20 × 20
Area of a square = 400 inch2
Further,
When the side of the square is increased by 8 times
Side of the new square = 8 × 20
Side of the new square = 160 inch
Now,
Area of the new square = side × side
Area of the new square = 160 × 160
Perimeter of the new square = 25600 inch2
Further,
To find how many times the area is increased
Increase in the area =
Increase in the area =
Increase in the area = 64 times
Therefore,
We can see that the area of the new square is 4 times the area of the original square
Thus,
The area of a square is increased by 64 times when its sides are increased by 8 times.
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