Which of the following are Pythagorean triplets-2 cm - 17 cm - 9 cm-24 cm - 10 cm - 26 cm-13 cm - 27 cm - 30 cm-4 cm - 6 cm - 8 cm-

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Standard X

Mathematics

Opposite & Adjacent Sides in a Right Angled Triangle

Which of the ...

Question

Which of the following are Pythagorean triplets?

4 cm , 6 cm , 8 cm

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2 cm , 17 cm , 9 cm

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24 cm , 10 cm , 26 cm

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13 cm , 27 cm , 30 cm

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Solution

The correct option is C
24 cm , 10 cm , 26 cm

Pythagorean triplets are those set of numbers which satisfy the Pythagoras theorem.

Considering the options given to us –

$8^{2} \neq 4^{2} + 6^{2}$

$17^{2} \neq 2^{2} + 9^{2}$

$26^{2} = 24^{2} + 10^{2}$

$30^{2} \neq 27^{2} + 13^{2}$

Therefore, 24, 10 and 26 are Pythagorean triplets.

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Question 20
Which of the following sets of triangles could be the lengths of the sides of a right-angled triangle?
a) 3 cm, 4 cm, 6 cm
b) 9 cm, 16 cm, 26 cm
c) 1.5 cm, 3.6 cm, 3.9 cm
d) 7 cm, 24 cm, 26 cm

Q. In which of the following cases, a right triangle cannot be constructed?
(a) 12 cm, 5 cm, 13 cm
(b) 8 cm, 6 cm, 10 cm
(c) 5 cm, 9 cm, 11 cm
(d) None of these

Q. The lengths of three segments are given for constructing a triangle. Say whether a triangle with these sides can be drawn. Give the reason for your answer.
(1) 17 cm, 7 cm, 8 cm (2) 7 cm, 24 cm, 25 cm
(3) 9 cm, 6 cm, 16 cm (4) 8.4 cm, 16.4 cm, 4.9 cm
(5) 15 cm, 20 cm, 25 cm (6) 12 cm, 12 cm, 16 cm

Q. The sides of certain triangles are given below. Determine which of them are right triangles.

(i) a = 7 cm, b = 24 cm and c = 25 cm
(ii) a = 9 cm, b = 16 cm and c = 18 cm
(iii) a = 1.6 cm, b = 3.8 cm and c = 4 cm
(iv) a = 8 cm, b = 10 cm and c = 6 cm

Q. In Fig. 4.60, check whether AD is the bisector of ∠A of ∆ABC in each of the following:

(i) AB = 5 cm, AC = 10 cm, BD = 1.5 cm and CD = 3.5 cm
(ii) AB = 4 cm, AC = 6 cm, BD = 1.6 cm and CD = 2.4 cm
(iii) AB = 8 cm, AC = 24 cm, BD = 6 cm and BC = 24 cm
(iv) AB = 6 cm, AC = 8 cm, BD = 1.5 cm and CD = 2 cm
(v) AB = 5 cm, AC = 12 cm, BD = 2.5 cm and BC = 9 cm

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Which of the following are Pythagorean triplets?

The correct option is C 24 cm , 10 cm , 26 cm Pythagorean triplets are those set of numbers which satisfy the Pythagoras theorem. Considering the options given to us – 82≠42+62 172≠22+92 262=242+102 302≠272+132 Therefore, 24, 10 and 26 are Pythagorean triplets.