# The area of a rectangle is 60 units. If the length and breadth are reduced respectively by 6 units

The area of a rectangle is 60 units. If the length and breadth are reduced respectively by 6 units and 2 units, it becomes a square. Then the area of the square (in sq. units) is

1. 4
2. 9
3. 16
4. 36
Anurag Mishra Professor Asked on 20th April 2016 in

Solution:-
Let the length and breadth of the rectangle be X and Y.

The area of a rectangle is 60 units.
Then, X Y = 60

If the length and breadth are reduced respectively  by 6 units and 2 units.
Then, X – 6 = Y – 2
X – Y = 6 – 2
X – Y = 4 ………………………. (1)
Square on both side,
(X – Y)^2 = X^2 + Y^2 – 2 X Y
4^2 = X^2 + Y^2 – 2 x 60
X^2 + Y^2 = 120 + 16
X^2 + Y^2 = 136 …………………… (2)

Again,
(X + Y)^2 = X^2 + Y^2 + 2 X Y
From equation (2),
(X + Y)^2 = 136 + 2 x 60
= 136 + 120
(X + Y)^2 = 256
Square root on both side,
X + Y = 16         ………………(3)

X – Y + X + Y = 16 + 4
2 X = 20
X = 10

Put the value of X = 10 in equation (3),
10 + Y = 16
Y = 16 – 10
Y = 6

Then, length and breadth of rectangle are 10 cm and 6 .

If the length and breadth are reduced respectively  by 6 units and 2 units.
Then, the side of the square = 10 – 6 = 4

So, the are of the square = 4 x 4
= 16 units

Hence, the correct answer is option (3) 16.

Anurag Mishra Professor Answered on 22nd April 2016.