Question

If the length of a rectangle is in-creased by 5 metres and breadth decreased by 3 metres, the area would decrease by 5 square metres. If the length is increased by 3 metres and breadth increased by 2 metres, the area would increase by 50 square metres. What are the length and breadth?

Answer 1

length = x; breadth = y

(x + 5)(y – 3) = xy – 5

xy – 3x + 5y – 15 = xy – 5

– 3x + 5y = + 10

3x – 5y = -10 ………..(1)

(x + 3)(y + 2) = xy + 50

xy + 2x + 3y + 6 = xy + 50

2x + 3y = 44 ………..(2)

(2) × 1 ⇒ 6x -10y = -20 ……….(3)

(3) × 2 ⇒ 6x + 9y = 132 …………(4)

(3) - (4) ⇒ -19y = -152

y = \(\frac{-152}{-19}\) = 8, 2x + 3y = 44 

2x + 24 = 44; 2x = 20; x = 10

∴ x = 10, y = 8

Length of the rectangle = 10 m

Breadth of the rectangle = 8m

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