Question

The area of a rectangle gets reduced by 8 m², when its length is reduced by 5 m and its breadth is increased by 3 m. If we increase the length by 3 m and breadth by 2 m, the area is increased by 74 m². Find the length and the breadth of the rectangle.

Answer 1

Let the length and the breadth of the rectangle be x m and y m, respectively.

∴ Area of the rectangle = (xy) sq.m

Case 1:

When the length is reduced by 5 m and the breadth is increased by 3 m:

New length = (x – 5) m

New breadth = (y + 3) m

∴ New area = (x – 5) (y + 3) sq.m

∴ xy – (x – 5) (y + 3) = 8

⇒ xy – [xy – 5y + 3x – 15] = 8

⇒ xy – xy + 5y – 3x + 15 = 8

⇒ 3x – 5y = 7   ...(i)

Case 2:

When the length is increased by 3 m and the breadth is increased by 2 m:

New length = (x + 3) m

New breadth = (y + 2) m

∴ New area = (x + 3) (y + 2) sq.m

⇒ (x + 3) (y + 2) – xy = 74

⇒ [xy + 3y + 2x + 6] – xy = 74

⇒ 2x + 3y = 68   ...(ii)

On multiplying (i) by 3 and (ii) by 5, we get:

9x – 15y = 21   ...(iii)

10x + 15y = 340    ...(iv)

On adding (iii) and (iv), we get:

19x = 361

⇒ x = 19

On substituting x = 19 in (iii), we get:

9 × 19 – 15y = 21

⇒ 171 – 15y = 21

⇒ 15y = (171 – 21)

⇒ 15y = 150

⇒ y = 10

Hence, the length is 19 m and the breadth is 10 m.