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.
To find this algebraically: let L be the length and W the width originally
A = L x W
When both are doubled, the equation becomes
A = [2L] x [2W] = 4LW
The area of the rectangle is quadrupled if both the length and width are doubled.
if you double the length and the width, you are quadrupling the area. this is because 2 * 2 = 4. 32 is 4 times as large as 8. you doubled the length and the width and you quadrupled the area.
Step-by-step explanation:
Question 488537: Suppose the length and width of the rectangle are doubled. what effect would this have on the area? Justify your answer. rectangle dimensions = 17ft L
4 ft W
Answer by Theo[12413]
You can put this solution on YOUR website!
A = L * W
this means area equals length times width.
if you double the length and you double the width, the formula becomes:
A = 2 * L * 2 * W which is the same as:
A = 2 * 2 * L * W which is the same as:
A = 4 * L * W
if you double the length and the width, you are quadrupling the area.
this is because 2 * 2 = 4.
an example:
L = 2 and W = 4
Area = 2 * 4 = 8
double the length and double the width to get:
L = 4 and W = 8
Area = 4 * 8 = 32
32 is 4 times as large as 8.
you doubled the length and the width and you quadrupled the area.
this is because 2 * 2 = 4
if you tripled the length and doubled the width, then the area would be 6 times as large because 2 * 3 = 6
an example:
L = 2 and W = 4
Area = 2 * 4 = 8
double the length and triple the width to get:
L = 4 and W = 12
Area = 4 * 12 = 48
48 is 6 times as big as 8.
what you did was:
L * W = Area
you doubled the length and tripled the width to get:
2 * L * 3 * W = Area
this becomes:
2 * 3 * L * W = Area which becomes:
6 * L * W = Area
the area becomes 6 times as large because 2 * 3 = 6.
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