linear equation of class-x

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Query:

Linear equation of class-x

Query Description:

THE AREA OF RECTANGLE GETS REDUCED BY 80CM2 IF ITS LENGTH IS REDUCED BY 5CM AND BREADTH IS INCREASED BY 2CM .IF WE INCREASE THE LENGTH BY 10CM AND DECREASE THE BREADTH BY 5CM,THE AREA IS INCREASED BY 50CM2.FIND THE LENGTH AND BREADTH

Answer:

Let L be the length and B be the breadth of the rectangle, then, area is LB (L - 5)(B + 2) = LB - 80 LB + 2L - 5B - 10 = LB - 80 2L - 5B = -70         Multiply by 2, 4L - 10B = -140       .... (1) Also, (L + 10)(B - 5) = LB + 50 LB - 5L + 10B - 50 = LB + 50  - 5L + 10B  = 100        ..... (2) Add (1) and (2), -L = - 40 L = 40 cm and therefore, B = (100 + 5x40)/10 = 30 cm. Hence the length is 40 cm and breadth is 30 cm. Regards, Team, TopperLearning.