22. The length of a rectangular field is increased by 3 m and breadth de-
creased by 3 m. Then the area decreased by 18 m². But if length and
breadth both are increased by 3 m. its area is increased by 60 m². Find the
length and breadth of the field ?
Answers
Step-by-step explanation:
Let the length and breadth of the rectangle be l and b respectively.
Then area of rectangle = ab
Case 1:-
If length is increased by 3
Length becomes = a + 3
If breadth is decreased by 3
Breadth becomes = b - 3
Then, The area decreases be 18m²
⇢ (a + 3)(b - 3) = ab - 18
⇢ ab - 3a + 3b - 9 = ab - 18
⇢ ab - ab - 3a + 3b = -18 + 9
⇢ -3a + 3b = -9
Dividing the whole equation by 3
⇢ b - a = -3.....(i)
Case 2:-
If length and breadth are increased by 3
The length becomes = a + 3
The breadth becomes = b + 3
The area is increased by 60m²
⇢ (a + 3)(b + 3) = ab + 60
⇢ ab + 3a + 3b + 9 = ab + 60
⇢ ab - ab + 3a + 3b = 60 - 9
⇢ 3a + 3b = 51
⇢ a + b = 17......(ii)
Adding equation (i) and (ii)
⇢ b - a + a + b = 17 - 3
⇢ 2b = 14
⇢ b = 7
Substituting b = 12 in equation (ii)
⇢ a + b = 17
⇢ a + 7 = 17
⇢ a = 17 - 7 = 10
We have:-
- a = 10
- b = 7
Therefore:-
⇝ The length of the rectangle = 10m
⇝ The breadth of the rectangle = 7m
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