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The area of rectangle is 297 so cm if its length is increased by 3 cm and width decreases by 1 cm its area increased by 3 cm. Find the length and width of rectangle:

The area of rectangle is 297 so cm if its length is increased by 3 cm and width decreases by 1 cm its area increased by 3 cm. Find the length and width of rectangle:

  • (A) 10 cm and 35 cm
  • (B) 11 cm and 27 cm
  • (C) 13 cm and 28 cm
  • (D) 15 cm and 35 cm
Solution:
  1. Let length = L, width = W. Equations:
    • ( L \times W = 297 )
    • ( (L + 3)(W - 1) = 300 )
  2. Expand second equation and substitute ( L \times W = 297 ): (-L + 3W = 6 \Rightarrow L = 3W - 6)
  3. Substitute into first equation: ((3W - 6) \times W = 297 \Rightarrow W^2 - 2W - 99 = 0)
  4. Solve quadratic: ( W = 11 ) → ( L = 3(11) - 6 = 27 )
Answer: 11 cm and 27 cm (B)
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