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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?
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- 1125
- 2250
- 2924
- 4500
Correct Option: B
Let the initial length of rectangle is l and breath is b. Now if length is reduced by 10 m and breath is reduced by 5 m then it becomes square.
∴ l – 10 = b – 5
[∵ In square length = breadth]
∴ l – b = 5
Given, initial, Area (A) = l × b
Now according to question,
(l – 10) (b – 5) = A – 650
∴ lb – 10b – 5l + 50 = A – 650
∴ A – 10b – 5l = A – 700
∴ 10b + 5l = 700
∴ 10b + 5 (b + 5) = 700
∴ 15b + 25 = 700
∴ 15b = 700 – 25
∴ 15b = 675
⇒ b = 45 m
∴ l = 45 + 5 = 50 m
∴ Area of original rectangle (A) = (45 × 50)m² = 2250 m².
