Question

What will happen to the area of a rectangle if its

(i) Length and breadth are trebled.
(ii) Length is doubled and breadth is same.
(iii) Length is doubled and breadth is halved.

Answer 1

(i) If the length and breadth of a rectangle are trebled.
Let the initial length and breadth be l and b, respectively.
Original area = l $\times$b = lb
Now, the length and breadth are trebled which means they become three times of their original value.
Therefore
New length = 3l
New breadth = 3b
New area = 3l $\times$3b = 9 lb
Thus, the area of the rectangle will become 9 times that of its original area.

(ii) If the length is doubled and the breadth is same.
Let the initial length and breadth be l and b, respectively.​
Original area = l $\times$b = lb
Now, length is doubled and breadth remains same.
Therefore
New length = 2l
New breadth = b
New area = 2l $\times$b = 2 lb
Thus, the area of the rectangle will become 2 times that of its original area.

(iii) If the Length is doubled and breadth is halved.
Let the initial length and breadth be l and b, respectively.​
Original area = l $\times$b = lb
Now, length is doubled and breadth is halved.
Therefore
New length = 2l
New breadth = b/2
New area = 2l $\times$b/2 = lb
New area is also lb. This means that the areas remain the same.