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Which of the following is a Pythagorean triplet? (a) 3, 4, 5 (b) 5, 12, 14 (c) 6, 8, 11 (d) 8, 5, 17

Which of the following is a Pythagorean triplet?
(a) 3, 4, 5
(b) 5, 12, 14
(c) 6, 8, 11
(d) 8, 5, 17

Grade:12th pass

1 Answers

Pawan Prajapati
askIITians Faculty 60787 Points
2 years ago
For solving this question we should know about the result of the Pythagoras Theorem in right-angled triangles. After that, we will examine every option separately and check whether it is a Pythagorean triplet or not. Complete step-by-step answer: Now, before we proceed just take a look at the result of the Pythagoras Theorem. The Pythagoras Theorem states that in a right-angled triangle as shown below ΔABC , the square of the hypotenuse is equal to the sum of the squares of the other two sides. In the ΔABC , ∠ACB=90∘ and AB is the hypotenuse, BC is the base and AC is the perpendicular. From Pythagoras Theorem, we have: (BC)2+(AC)2=(AB)2⇒a2+b2=c2 Then, we can write, (base)2+(perpendicular)2=(hypotenuse)2. Now, we can easily understand the concept of the Pythagorean triplet. Pythagorean Triplet: Pythagorean triplet are the values of hypotenuse, base and perpendicular which tend to represent a right-angled triangle. Integral solutions to the Pythagorean Theorem, a2+b2=c2 are called Pythagorean triplet which contains three positive integers a,b,c where a

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