Question

If the length and breadth of a rectangular floor are increased by 2 metres, its area would be 36m² more, if the length is increased by 5 meters and the breadth is decreased by 2 meters, its area will remain unaltered. Find the length and breadth of the floor.​

Answer 1

Answer:

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Answer 2

Answer:

length = 10 , breadth = 6

Step-by-step explanation:

let length be L and breadth be B

so ,

=> (L + 2) (B + 2) = LB + 36

=> LB + 2L + 2B + 4 = LB + 36

=> LB - LB +2L + 2B = 36 - 4

=> 2L + 2B = 32

=> 2(L + B) = 32

=> L + B = 32/2

=> L + B = 16

Also ,

=> (L + 5) (B - 2) = LB

=> LB - 2L + 5B - 10 = LB

=> LB - LB - 2L + 5B - 10 = 0

=> -2L + 5B - 10 = 0

=> 5B = 10 + 2L

=> B = (10 + 2L) / 5

Now ,

L + B = 16

B = (10 + 2L) / 5

=> L + ( (10 + 2L) / 5) = 16

=> ( 5L + 10 + 2L ) / 5 = 16

=> 7L + 10 = 16 * 5

=> 7L + 10 = 80

=> 7L = 70

=> L = 10

=> L + B = 16

=> 10 + B = 16

=> B = 16 -10

=> B = 6

L = 10 , B = 6