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MHT CET202619 April 2026Morning ShiftMathematicsThree Dimensional GeometryActual

The plane x 2 + y 3 + z 4 = 1 cuts the axes at the points A, B, C then the area of triangle ABC is

Options

  1. A29
  2. B41
  3. C61
  4. D51

Correct answer

C. 61

Step-by-step solution

The plane x 2 + y 3 + z 4 = 1 intersects the coordinate axes at A(2, 0, 0) , B(0, 3, 0) , and C(0, 0, 4) . The area of ABC is given by = _ xy ^2 + _ yz ^2 + _ zx ^2 , where _ xy , _ yz , and _ zx are the areas of the projections of ABC on the xy , yz , and zx planes respectively. _ xy = 1 2 2 3 = 3 _ yz = 1 2 3 4 = 6 _ zx = 1 2 4 2 = 4 = 3^2 + 6^2 + 4^2 = 9 + 36 + 16 = 61 Answer: 61

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