Question

What is the greatest possible perimeter of a right-angled triangle with integer side lengths of one of the sides has length 12 ?

Answer 1

Solution :-

Let us assume that the length of the shortest side of the right angled triangle is 12 cm

Then, we can find the length of the other two sides by the formula of Pythagorean Triplet. The formula is (2m, m² - 1 and m² + 1)

⇒ 2m = 6

⇒ m = 6/2

⇒ m = 6

m² - 1

⇒ 6² - 1

⇒ 36 - 1 

 35 cm

m² + 1

⇒ 6² + 1

⇒ 36 + 1

⇒ 37 cm

So, the three  sides of the right angled triangle are 12 cm, 35 cm and 37 cm

Perimeter of the scalene triangle = a + b + c

⇒ 12 + 35 + 37

Perimeter = 84 cm

Answer.