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Which of the following statements cannot be true?
I. If the length of the sides of a right angled triangle are in arithmetic progression, the length of one of its sides can be 1809 units.
II. A primitive Pythagorean triplet is one where the GCD of the three numbers in the triplet is 1. If an integer greater than 25 belongs to a Pythagorean triplet, then that triplet is non-primitive.
III. The area of a right angled triangle will always be an odd integer.  
  • a)
    I only
  • b)
    II only
  • c)
    II and III
  • d)
    I and II
Correct answer is option 'C'. Can you explain this answer?
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Which of the following statements cannot be true?I. If the length of t...
Statement I is correct: If (a, b, c) is a Pythagorean triplet then (ka, kb, kc) is also a Pythagorean triplet for any natural number k. (3, 4, 5) is a Pythagorean triplet. (3k, 4k, 5k) will also be a Pythagorean triplet for any natural number k.
(1809, 2412, 3015) is a Pythagorean triplet (for k = 603) and 1809, 2412 and 3015 are in A.P.
Statement II is incorrect: (28, 45, 53) is a primitive Pythagorean triplet with length of all the sides greater than 25.
Statement III is incorrect: For the right angled triangle with length of sides 3, 4 and 5, its area = 1/2 x 3 x 4 = 6 square units, which is even. Moreover, the area of a right triangle need not always be an integer value.
Hence, option 3.
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Which of the following statements cannot be true?I. If the length of the sides of a right angled triangle are in arithmetic progression, the length of one of its sides can be 1809 units.II. A primitive Pythagorean triplet is one where the GCD of the three numbers in the triplet is 1. If an integer greater than 25 belongs to a Pythagorean triplet, then that triplet is non-primitive.III. The area of a right angled triangle will always be an odd integer. a)I onlyb)II onlyc)II and IIId)I and IICorrect answer is option 'C'. Can you explain this answer?
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