# The area of a rectangle gets increased by 30 square units, if its length is reduced by 3 units and breadth is increased by 5 units. If we increase the length by 5 units and reduce the breadth by 3 units then the area of a rectangle reduces by 10 square units. Find the length and breadth of the rectangle.

Let the length be x units and breadth be y units of a rectangle.

Area of rectangle = x × y

According to the question,

If length is reduced by 3, length = (x – 3)

Area = (xy + 30)

(x – 3)(y + 5) = (xy + 30)

xy + 5x – 3y – 15 = xy + 30

5x – 3y = 45 …(i)

If length is incresed by 5, length = (x + 5)

Area = (xy – 10)

(x + 5)(y – 3) = (xy – 10)

xy – 3x + 5y – 15 = xy – 10

– 3x + 5y = 5 …(ii)

Multiply (i) by 3 and (ii) by 5,

15x – 9y = 135 .. (iii)

– 15x + 25y = 25 …(iv)

15x – 9y – 15x + 25y = 135 + 25

16y = 160

y = 10

Putting this in (i),

5x – 3×10 = 45

5x = 45 + 30

5x = 75

x = 15

So, the length is 15 units and breadth is 10 units.

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