# What is the area of the rectangle:

If the length of a rectangle is increased by 20 % and width of the same rectangele decreased by 20 %, then the area of the rectangle:

1. Decreases by 20%
2. Decreases by 4%
3. Is unchanged
4. Increases by 20 %
Harsh Vardhan Professor Asked on 25th October 2015 in

Answer:  (2)  Decreased by 4 %

Explanation:-
Let the length of a rectangle is  X m and width of the same rectangle is Y m
Then, the area of the rectangle = X Y square m

If the length of a rectangle is increased by 20 %
Then, the length of a new rectangle = X + X x 20/100
= X + X/5
= (5 x + X)/5
= 6 X/5 m

If the breadth of the rectangle is decreased by 20 %
Then, the new breadth of the rectangle = Y – Y  x 20/100
= Y – Y/5
= (5 Y – Y)/5
= 4 Y/5

Then, the area of new rectangle = 6 X x 4 Y /5 x
= 24 X Y /25

Decreased area = X Y- 24 X Y /25
= (25 X Y – 24 X Y)/25
= X Y/25

Decreased area in percentage = X Y x 100/25 x X Y
= 100/25 %
= 4 %

Then, the area of a rectangle is decreased by 4%.

Hence, the answer is (2) 4%.

Anurag Mishra Professor Answered on 25th October 2015.