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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