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When the length of rectangle is decreased by 10ft. and the breadth is increased by 5 feet, the rectangle becomes a square and its area is reduced by 210 square feet. Find the area of the rectangle.
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- 2440 square feet
- 2340 square feet
- 2444 square feet
- 2540 square feet
- 2440 square feet
Correct Option: C
Let the length and breadth of rectangle be x and y feet respectively.
Area of rectangle = xy
Again, x – 10 = y + 5 = side of square
⇒ x = y + 15 ....(i)
Again, xy – (y + 5)² = 210
⇒ y (y + 15) – (y² + 10y + 25) = 210
⇒ y² + 15y – y² – 10y – 25 = 210
⇒ 5y = 235
⇒ y = 47 feet
∴ x = y + 5 = 52 feet
Area of rectangle = 52 × 47 = 2444 sq. feet
