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AP EAMCET20224 Jul 2022Morning ShiftMathematicsStraight LinesActual

Suppose a triangle is formed by x + y = 10 and the coordinate axes. Then the number of points x , y where x and y are natural numbers, lying inside the triangle is

Options

  1. A36
  2. B55
  3. C45
  4. D30

Correct answer

A. 36

Step-by-step solution

Plotting the diagram of the given value we have, Triangle formed will have vertices as O 0 , 0 ,   A 10 , 0 and B 0 , 10 If x = 1 , Point on the hypotenuse ≡ 1 , 9 So, number of integral points lying inside triangle when x = 1 is 8 i.e 1 , 1 , 1 , 2 ⋯ 1 , 8 Similarly, when x = 2 , number of integral points lying inside triangle is 7 i.e 2 , 1 , 2 , 1 ⋯ 2 , 7 ∴ Total number of integral points lying inside triangle are = 8 + 7 + 6 + … + 1 = 8 × 9 2 = 36

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