# 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

- 4
- 9
- 16
- 36

**Answer: (3) 16 **

**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)

Add equation (1) & (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.