Question

write a Pythagorean triplet whose one of the number is 6​

Answer 1

Answer:

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Answer 2

$\mathfrak{\large{\underline{\underline{Answer :-}}}}$

The Pythagorean triplet is 6, 8 and 10.

$\mathfrak{\large{\underline{\underline{Explanation :-}}}}$

Given :

Number to be included in the Pythagorean triplet = 6

To Find :

Pythagorean triplet whose one of the number is 6

Solution :

Pythagorean triplet for any number when m > 1

$\sf{2m,{m}^{2} + 1 \: and \: {m}^{2} - 1}$ is a Phythagorean Triplet.

The smallest Number in the Pythagorean triplet is 2m.

Let 6 be the Smallest number in the Pythagorean triplet.

★ $\boxed{\bf{2m,{m}^{2} + 1 \: and \: {m}^{2} - 1}}$

$\tt{\longrightarrow} \: 2m = 6 \\ \tt{\longrightarrow} \: m = \frac{6}{2} \\ \tt{\longrightarrow} \: m = 3$

$\rule{300}{1.5}$

★ m² - 1

$\tt{\longrightarrow} \: {m}^{2} - 1$

$\tt{\longrightarrow} \: {3}^{2} - 1$

$\tt{\longrightarrow} \: 9 - 1$

$\tt{\longrightarrow} \: 8$

Second Number = 8

$\rule{300}{1.5}$

★ m² + 1

$\tt{\longrightarrow} \: {m}^{2} + 1$

$\tt{\longrightarrow} \: {3}^{2} + 1$

$\tt{\longrightarrow} \: 9 + 1$

$\tt{\longrightarrow} \: 10$

Third Number = 10

$\therefore$ The Pythagorean triplet is 6, 8 and 10.

$\rule{300}{1.5}$

$\mathfrak{\large{\underline{\underline{Verification :-}}}}$

Verify that is 6, 8 and 10 is a Pythagorean triplet or not.

By Pythagoras theorem -

10 will be the hypotenuse as it is the the longest of both.

★ (Hypotenuse)² = (Base)² + (Height)²

$\tt{\longrightarrow} \: {10}^{2} = {6}^{2} + {8}^{2}$

$\tt{\longrightarrow} \: 100 = 64 + 36$

$\tt{\longrightarrow} \: 100 = 100$

$\therefore$ The Pythagorean triplet is 6, 8 and 10.