Q. 4 A rectangle becomes a square when its length and breadth are reduced by 10 m and 5 m, respectively.
During this process, the rectangle loses 650 m² of area. What is the area of the original rectangle
in square meters?
A rectangle has its length reduced by 10 meters and breadth reduced by 5 meters,
after which it becomes a square. Due to this reduction, the area decreases by
650 square meters. Find the original area of the rectangle.
Correct Answer: 2250 m² (Option B)
Step-by-Step Solution
Let the original length be L meters and breadth be B meters.
Since the new figure is a square:
L − 10 = B − 5
⇒ L = B + 5
Area lost:
LB − (L − 10)(B − 5) = 650
Expand the reduced area:
(L − 10)(B − 5) = LB − 5L − 10B + 50
Substitute into loss equation:
LB − (LB − 5L − 10B + 50) = 650
Simplifying:
5L + 10B − 50 = 650
5L + 10B = 700
L + 2B = 140
Substitute L = B + 5:
(B + 5) + 2B = 140
3B + 5 = 140
3B = 135
B = 45
L = 50
Original Area:
Area = 50 × 45 = 2250 m²
Options Analysis
| Option | Area (m²) | Length (m) | Breadth (m) | New Length (m) | New Breadth (m) | New Area (m²) | Loss (m²) | Matches? |
|---|---|---|---|---|---|---|---|---|
| (A) | 1125 | 45 | 25 | 35 | 20 | 700 | 425 | No |
| (B) | 2250 | 50 | 45 | 40 | 40 | 1600 | 650 | Yes |
| (C) | 2924 | ~54.1 | ~54.1 | 44.1 | 49.1 | Not square | N/A | No |
| (D) | 4500 | 90 | 50 | 80 | 45 | 3600 | 900 | No |
Why Option (B) Is Correct
- After reduction, the figure becomes a square (40 × 40)
- Exact area loss equals 650 m²
- Original dimensions satisfy all conditions
Final Answer: 2250 square meters
