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If the length of a rectangle is decreased by 5 metres and breadth increased by 3 metres, its area decreases by 9 m2. If its length is increased by 3 m and breadth by 2 m,its area increases by 67 m2. What is the length of a rectangle ?
  • a)
    8 m
  • b)
    15.6 m
  • c)
    17 m
  • d)
    18.5 m
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
If the length of a rectangle is decreased by 5 metres and breadth incr...
(l - 5)(b+3) = lb - 9 .... (1)
(l+ 3)(b+2) = lb + 67 ...... (2)
(1) => lb - 5b + 3l -15 = lb - 9
or 3l - 5b = 6
(2) = > lb + 3b + 2l + 6 = lb + 67
or 2l + 3b = 61
from these equations, l = 17 m
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Most Upvoted Answer
If the length of a rectangle is decreased by 5 metres and breadth incr...

Given information:

- Let the original length of the rectangle be L meters and the original breadth be B meters.
- When the length is decreased by 5 meters and breadth is increased by 3 meters, the area decreases by 9 square meters.
- When the length is increased by 3 meters and breadth is increased by 2 meters, the area increases by 67 square meters.

Calculations:

1. From the first condition:
- (L - 5)(B + 3) = LB - 9
- LB + 3L - 5B - 15 = LB - 9
- 3L - 5B = 6 ...(i)

2. From the second condition:
- (L + 3)(B + 2) = LB + 67
- LB + 2L + 3B + 6 = LB + 67
- 2L + 3B = 61 ...(ii)

3. Solving equations (i) and (ii):
- Multiplying equation (i) by 2 and adding it to equation (ii):
- 6L - 10B + 2L + 3B = 12 + 61
- 8L - 7B = 73
- 8L = 7B + 73 ...(iii)

4. Substitute the value of B from equation (iii) into equation (i):
- 3L - 5(7B + 73)/8 = 6
- 3L - 35B/8 - 365/8 = 6
- 3L - 35B - 365 = 48
- 3L = 35B + 413

5. Substitute the values into the equation:
- 3L = 35B + 413
- 3L = 35(8) + 413
- 3L = 280 + 413
- 3L = 693
- L = 231

Therefore, the length of the rectangle is 231 meters, which is closest to option (C) 17 meters.
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If the length of a rectangle is decreased by 5 metres and breadth increased by 3 metres, its area decreases by 9 m2. If its length is increased by 3 m and breadth by 2 m,its area increases by 67 m2. What is the length of a rectangle ?a)8 mb)15.6 mc)17 md)18.5 mCorrect answer is option 'C'. Can you explain this answer?
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