Out of the dates given below which date constitutes a Pythagorean triplet ?
15/08/17
16/08/16
3/5/17
4/9/15
Chapter 2 – Pythagoras Theorem- Text Book Solution
Problem Set 2 | Q 1.3 | Page 43
Some question and their alternative answer are given. Select the correct alternative.
Out of the dates given below which date constitutes a Pythagorean triplet ?
15/08/17
16/08/16
3/5/17
4/9/15
Solution
(A) In the triplet 15/08/17,
152 = 225, 82 = 64, 172 = 289 and 225 + 64 = 289
The square of the largest number is equal to the sum of the squares of the other two numbers.
∴ 15/08/17 is a pythagorean triplet.
Explanation:-
The concept of Pythagorean triplets is related to the Pythagoras theorem, which states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
So, for a triplet to be a Pythagorean triplet, it should satisfy this condition. Let’s check the given dates to see if they form a Pythagorean triplet:
-
15/08/17: This is a date and cannot form a Pythagorean triplet.
-
16/08/16: This is a date and cannot form a Pythagorean triplet.
-
3/5/17: This is not a valid representation of a right-angled triangle, as it does not give the length of the sides. Therefore, it cannot form a Pythagorean triplet.
-
4/9/15: Here, we can consider 4, 9, and 15 as the lengths of the sides of a right-angled triangle. Checking the condition of the Pythagoras theorem, we have:
Hypotenuse^2 = 15^2 = 225 Sum of squares of other two sides = 4^2 + 9^2 = 16 + 81 = 97
Since the sum of the squares of the other two sides is not equal to the square of the hypotenuse, 4/9/15 does not form a Pythagorean triplet.
Therefore, the correct answer is none of the given dates form a Pythagorean triplet.
Chapter 2 – Pythagoras Theorem- Text Book Solution
Problem Set 2 | Q 1.3 | Page 43