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Three consecutive integers form the lengths of a right-angled triangle. How many sets of such three consecutive integers is/are possible?
- a)Only one
- b)Only two
- c)Only three
- d)Infinitely many
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Three consecutive integers form the lengths of a right-angled triangle...
let n-1, n, n+1 be 3 consecutive integers
So
(n+1)2 = n2 + (n-1)2
(n+1)2- (n-1)2 = n2
4n = n2
So n = 0 or n = 4
n can’t be 0 as n-1 will be negative then
So 3,4 and 5 is the only triplet formed
So
(n+1)2 = n2 + (n-1)2
(n+1)2- (n-1)2 = n2
4n = n2
So n = 0 or n = 4
n can’t be 0 as n-1 will be negative then
So 3,4 and 5 is the only triplet formed
Most Upvoted Answer
Three consecutive integers form the lengths of a right-angled triangle...
let n-1, n, n+1 be 3 consecutive integers
So
(n+1)2 = n2 + (n-1)2
(n+1)2- (n-1)2 = n2
4n = n2
So n = 0 or n = 4
n can’t be 0 as n-1 will be negative then
So 3,4 and 5 is the only triplet formed
So
(n+1)2 = n2 + (n-1)2
(n+1)2- (n-1)2 = n2
4n = n2
So n = 0 or n = 4
n can’t be 0 as n-1 will be negative then
So 3,4 and 5 is the only triplet formed
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Three consecutive integers form the lengths of a right-angled triangle. How many sets of such three consecutive integers is/are possible?a)Only oneb)Only twoc)Only threed)Infinitely manyCorrect answer is option 'A'. Can you explain this answer?
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Solutions for Three consecutive integers form the lengths of a right-angled triangle. How many sets of such three consecutive integers is/are possible?a)Only oneb)Only twoc)Only threed)Infinitely manyCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Defence.
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