Identify, with reason, if the following is a Pythagorean triplet. (10, 24, 27)
Practice Set 2.1 | Q 1.5 | Page 38
Identify, with reason, if the following is a Pythagorean triplet.
(10, 24, 27)
In the triplet (10, 24, 27),
102 = 100, 242 = 576, 272 = 729 and 100 + 576 = 676 ≠ 729
The square of the largest number is not equal to the sum of the squares of the other two numbers.
∴ (10, 24, 27) is not a pythagorean triplet.
Explanation:-
No, (10, 24, 27) is not 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 (10, 24, 27), the two shorter sides of the triangle are 10 and 24, and the longest side (the hypotenuse) is 27.
Using the Pythagorean theorem, we can verify that:
10^2 + 24^2 = 100 + 576 = 676
27^2 = 729
Since 729 is not equal to 676, we see that (10, 24, 27) does not satisfy the Pythagorean theorem, and hence is not a Pythagorean triplet.
Chapter 2 – Pythagoras Theorem- Text Book Solution
Practice Set 2.1 | Q 1.5 | Page 38