# Mathematics Questions and Answers – Pythagorean Triplet

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This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Pythagorean Triplet”.

1. Which of the following is the first Pythagorean triplet?
a) 3, 4 & 5
b) 12, 13 & 15
c) 6, 8 & 10
d) 1, 2 & 3

Explanation: Pythagorean triples are the numbers that follow a certain pattern. The pattern is that the square of the biggest amongst three is the sum of square of other two. This condition is satisfied by only one option i.e. 3, 4 & 5, hence this is the correct option and the others are incorrect.

2. In a right angled triangle if one side forming the right angle is 6 and the hypotenuse is 10. What is the length of the other right angle forming side?
a) 8
b) 10
c) 12
d) 6

Explanation: In a right angle triangle we can use Pythagoras theorem. This theorem states that the square of the hypotenuse is equal to the sum of squares of the other two right angle forming sides. Let us assume the one of the sides of the right angled triangle be x.
∴ 62+x2=102,
∴ x2=100-36,
∴ x=8.

3. Pythagoras theorem can only be applied on ________ triangles.
a) equilateral
b) isosceles
c) right angled
d) isosceles right angled

Explanation: Pythagoras theorem can only be used on right angles triangles. As a result only the option stating right angled triangles would be correct and the others would be incorrect.
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4. 3, 4 & 5 are not a Pythagorean triplet.
a) True
b) False

Explanation: If we consider 32+42 to be L.H.S. and 52 to be R.H.S. we get,
L.H.S.= 32+42,
L.H.S.=25.
Now, we take R.H.S.
R.H.S.=52=25.
Hence L.H.S.=R.H.S.
Hence the given triplet is a Pythagorean triplet a

5. 3, 4 & 6 is a Pythagorean triplet.
a) True
b) False

Explanation: If we consider 32+42 to be L.H.S. and 62 to be R.H.S. we get,
L.H.S.= 32+42,
L.H.S.=25.
Now, we take R.H.S.
R.H.S.= 62=36.
L.H.S.≠R.H.S.

6. Which of the following is not a Pythagorean triplet?
a) 12, 16, 20
b) 21, 28, 35
c) 33, 44, 55
d) 4, 5, 6

Explanation: The option which has 4, 5, 6 is not a Pythagorean triplet, and the other options are the multiples of it.

7. In the below figure, ABC is a right angled triangle and the lengths AB = 12, BC = 5, What would be the length of AC? a) 13
b) 12
c) 5
d) 169

Explanation: Here the given triangle is a right angled triangle, we can use Pythagoras theorem. Theorem will help us find the length of side AC.
Using Pythagoras Theorem we get,
122+52= AC2,
AC=13.

8. Which of the following is a Pythagorean triplet?
a) 10, 6 & 8
b) 13, 14 & 15
c) 7, 8 & 10
d) 5, 2 & 3

Explanation: Pythagorean triples are the numbers that follow a certain pattern. The pattern is that the square of the biggest amongst three is the sum of square of other two. This condition is satisfied by only one option i.e. 10, 6 & 8, hence this is the correct option and the others are incorrect.

9. In a right angle ∆ABC, AB=12, BC=5 and Angle ABC=90°. Find AC.
a) 169
b) 13
c) 17
d) 14

Explanation: This triangle is a right angled triangle so we can use Pythagoras theorem. Therefore, we get
∴ AC2 = AB2 + BC2
∴ AC2 = 122 + 52
∴ AC2 = 144 + 25
∴ AC2 = 169
∴ AC = 13.

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