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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.

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Solution

## 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) = 150 ⇒ y = 10 Hence, the length is 19 m and the breadth is 10 m.

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