Question

find the Pythagorean triplet whose smallest number is 14

Answer 1

m, m^2-1, m^2+1
m = 14÷2 = 7
7 , 7^2-1 , 7^2+1
7 , 48 , 50
14,48,50

Answer 2

Answer:

The Pythagorean triplet is 14, 48 and 50

Step-by-step explanation:

Given :

Smallest number required = 14

Solution :

We know that -

A Pythagorean triplet is -

• 2m
• m² + 1
• m² - 1

The Smallest Number is 2m.

So,

➙ 2m = 14

➙ m = 14/2

➙ m = 7

$\rule{300}{1.5}$

Value of m² + 1

➙ (7)² + 1

➙ 49 + 1

➙ 50

$\rule{300}{1.5}$

Value of m² - 1

➙ (7)² - 1

➙ 49 - 1

➙ 48

$\therefore$ The Pythagorean triplet is 14, 48 and 50

$\rule{300}{1.5}$

Verification :-

★ (Hypotenuse)² = (Base)² + (Height)²

Hypotenuse is always the longest side.

➙ (50)² = (48)² + (14)²

➙ 2500 = 2304 + 196

➙ 2500 = 2500

➙ LHS = RHS

$\therefore$ The Pythagorean triplet is 14, 48 and 50