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Pythagorean Triple

If three numbers are such that the square of the largest one is equal to the sum of the squares of
other two, then they are known as Pythagorean Triples.
The few examples of Pythagorean Triples are: Quick Check
2
2
2
(i) 3, 4, 5 [5 = 3 + 4 ] Find the value of k, if
2
2
2
(ii) 5, 12, 13 [13 = 5 + 12 ] (8, 15, k) is a Pythagorean
2
2
2
(iii) 7, 24, 25 [25 = 7 + 24 ] triplet.
Example 12: DABC is right-angled at C. If AC = 6 cm and BC = 8 cm, find the length of AB.
Solution: In right-angled triangle ABC, right-angled at C, by Pythagoras property,
2
2
AB = AC + BC 2 A
2
2
AB = 6 + 8 2
2
AB = 36 + 64 6 cm ?
2
AB = 100
2
AB = 10 × 10 C 8 cm B
2
2
AB = 10 . So, AB = 10
Thus, the length of the side AB = 10 cm.
Example 13: Find the value of x in the following:
A
B
12 cm
(a) x m 26 m (b) x cm
C
A 15 cm
B 24 m C

Solution: (a) In right-angled triangle ABC, right-angled at B, by Pythagoras property,
2
2
AC = AB + BC 2
2
2
26 = AB + 24 2 A
2
AB = 676 – 576
2
AB = 100 x m 26 m
2
AB = 10 × 10
AB = 10 2 B 24 m C
2
So, AB = 10 m
Thus, x = 10
(b) In right-angled triangle ABC, right-angled at B, by Pythagoras property,
2
2
AC = AB + BC 2
15 = x + 12 2
2
2
2
AB = 225 – 144 B
AB = 81 x cm 12 cm
2
AB = 9 × 9 C
2
AB = 9 2 A 15 cm
2
So, AB = 9 m
Thus, x = 9

183 The Triangle and Its Properties