Question

What happens to the area of a rectangle when length is halved and breadth is doubled ?

Answer 1

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.