Identify, with reason, if the following is a Pythagorean triplet. (4, 9, 12)
Practice Set 2.1 | Q 1.2 | Page 38
Identify, with reason, if the following is a Pythagorean triplet.
(4, 9, 12)
In the triplet (4, 9, 12),
42 = 16, 92 = 81, 122 = 144 and 16 + 81 = 97 ≠ 144
The square of the largest number is not equal to the sum of the squares of the other two numbers.
∴ (4, 9, 12) is not a pythagorean triplet.
Answer:-
Yes, (4, 9, 12) is a Pythagorean triplet.
A Pythagorean triplet is a set of three positive integers that satisfy the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In the given set (4, 9, 12), the two shorter sides of the triangle are 4 and 9, and the longest side (the hypotenuse) is 12.
Using the Pythagorean theorem, we can verify that:
4^2 + 9^2 = 16 + 81 = 97
12^2 = 144
Since 12^2 = 4^2 + 9^2 = 97, we see that (4, 9, 12) satisfies the Pythagorean theorem, and hence is a Pythagorean triplet.
Chapter 2 – Pythagoras Theorem- Text Book Solution
Practice Set 2.1 | Q 1.2 | Page 38