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The area of the square ABCD is 64. Let E, F and G be midpoints of DC, AD and BC respectively. If P is any point inside the rectangle ABGF and if X is the area of the triangle DPE, then which one of the following is necessarily true?
  • a)
    8 < x="" />< />
  • b)
    8 < x="" />< />
  • c)
    16 < x="" />< />
  • d)
    16< x="" />
  • e)
    None of these
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
The area of the square ABCD is 64. Let E, F and G be midpoints of DC,...
CD = 8
Hence, DE = 4
If P lies on AB,
Area of DPE = X = ½ X 4 X 8 = 16
If P lies on GF,
Area of DPE = X = ½ X 4 X 4 = 8
Hence, X lies between 8 and 16
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