What happens to the perimeter of a rectangle when its width and length are doubled?

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• What happens to the area of a rectangle if its length is doubled?
• How does doubling the length and width of a rectangle affect its area?
• What will happen to the area of a square if its sides are doubled halved?
• What happens to the area of a rectangle when the length is doubled and the width is tripled?

Hint: In order to determine how the area changes when it is length is halved and breadth is doubled.
First of all we will find the area of the rectangle then we will find the new area of the rectangle when length is halved and breadth is doubled.
We will use the formula that the area of the rectangle is given by \[area = l \times b\].

Complete step-by-step answer:
We need to find the area of a rectangle when length is halved and breadth is doubled
Let \[ABCD\] be a rectangle whose sides are \[AB = l \] cm and \[BC = b\] cm.
Then \[AB = CD\] and \[BC = AD\] .
Area of rectangle ABCD = Length \[ \times \] breadth
\[area = l \times b \; c{m^2}\]
Now, let the length be halved and breadth be doubled
So new \[length = \dfrac{l}{2}\] ,
New \[breadth = 2b\]
Then new area = length x breadth
i.e. \[area = \dfrac{l}{2} \times 2b = l \times b \; c{m^2}\]
Hence we see that the new area is the same as the old area.
Therefore, the area of the rectangle will be the same when the length is halved and breadth is doubled.
So, the correct answer is “SAME”.

Note: Rectangle is a closed figure bounded by the \[4\] line segment whose opposite sides are equal.
For example: let \[ABCD\] be a rectangle, then side \[AB = {\text{ }}CD\] and \[BC = {\text{ }}AD\] .
Area of the rectangle is given by product of length and breadth.
i.e. Area = length x breadth.
Perimeter [i.e. the length of the outer boundary of the rectangle ] is given by formula
Perimeter = \[2\left[ {l + b{\text{ }}} \right]\] , where \[l\] is length and \[b\] is breadth of the rectangle.
If the sides of the rectangle are equal then the rectangle is said to be a square. A square is a closed figure bounded by the \[4\] line segment whose all sides are equal .
Hence all squares are rectangles but all rectangles are not squares.

What happens to the area of a rectangle if its length is doubled?

Hence, area of rectangle become 2 t i m e s when length is doubled and breadth remains same. [i] Length and breadth are trebled.

How does doubling the length and width of a rectangle affect its area?

⇒ If the length and the breadth of a rectangle are doubled then its area becomes 4 times.

What will happen to the area of a square if its sides are doubled halved?

Hence, area of square becomes 4 t i m e s when side is doubled.

What happens to the area of a rectangle when the length is doubled and the width is tripled?

Ans — Area of Rectangle is 6 times more.

Question 515421: If the length and width of a rectangle are doubled, how do the perimeters of the original and new rectangles compare?
Found 2 solutions by richard1234, oberobic:Answer by richard1234[7193]   [Show Source]:

You can put this solution on YOUR website!
The perimeter of the new rectangle is double. To show this algebraically, we let L and W be the length, width of the original rectangle. The perimeter is 2L + 2W. The new rectangle would have dimensions 2L and 2W, and the perimeter would be 2[2L ] + 2[2W] = 4L + 4W, or double the original perimeter.

Answer by oberobic[2304]   [Show Source]:

You can put this solution on YOUR website!
P = perimeter = 2[L+W] = 2L + 2W
A = area = L*W
.
If you double L and W, you have 2L and 2W
so
P = 2[2L + 2W] = 4L + 4W
which means the perimeter has doubled from 2L + 2W to 4L + 4W.
.
A = 2L*2W
A = 4L*W
.
However, the area has quadrupled.
Why?
2*2 = 4
.
As a check, consider a rectangle with sides = 4 ft.
[Yes, it's a square.]
.
P = 2[4+4] = 2[8] = 16 ft
A = 4*4 = 16 sq ft
.
Now double the sides = 8 ft
.
P = 2[8+8] = 2*16 = 32
A = 8*8 = 64
.
The perimeter doubled from 16 to 32 ft.
The area quadrupled from 16 to 64.
.
Done.

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