Which of the following is a Pythagoras triplet?

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

3, 4, 5

5, 12, 14

6, 8, 11

8, 5, 17

answer is A.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Let us take the first option
(1) 3, 4, 5
We know that the largest side is the hypotenuse and the remaining lengths are sides of right angles triangle
By using the above condition we get that 5 is hypotenuse and 3, 4 are the remaining sides of the triangle.
We know that the Pythagoras Theorem states that the square of the hypotenuse is equal to sum of squares of the other two sides that is for the triangle shown below
Question Image

The Pythagoras theorem is given as

b^{2} = a^{2} + c^{2}

.By using the above theorem to given triplet we get
⇒

5^{2} = 3^{2} + 4^{2}

⇒25=9+16
⇒25=25
Here, we can see that LHS is equal to RHS
Therefore, we can conclude that the triplet 3, 4, 5 is a Pythagoras triplet.
(2) 5, 12, 14
Here, we can see that 14 is hypotenuse and 5, 12 are the remaining sides.
By using the Pythagoras theorem then we get
⇒

14^{2} = 5^{2} + 12^{2}

⇒196=25+144
⇒196=169
Here, we can see that LHS is not equal to RHS
Therefore, we can conclude that the triplet 5, 12, 14 is not a Pythagoras triplet.
(3) 6, 8, 11
Here, we can see that 11 is hypotenuse and 6, 8 are the remaining sides.
By using the Pythagoras theorem then we get
⇒

11^{2} = 6^{2} + 8^{2}

⇒121=36+64
⇒121=100
Here, we can see that LHS is not equal to RHS
Therefore, we can conclude that the triplet 6, 8, 11 is not a Pythagoras triplet.
(4) 8, 5, 17
Here, we can see that 17 is hypotenuse and 5, 8 are the remaining sides.
By using the Pythagoras theorem then we get
⇒

17^{2} = 5^{2} + 8^{2}

⇒289=25+64
⇒289=89
Here, we can see that LHS is not equal to RHS
Therefore, we can conclude that the triplet 5, 8, 17 is not a Pythagoras triplet.
So, we can say that 3, 4, 5 is the only Pythagoras triplet given
Therefore, option (1) is the correct answer.

Watch 3-min video & get full concept clarity