Question

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

Answer 1

using Pythagorean triplets (2m;m^2-1,if we take 2=12mthen m=6thus m^2-1=37 so perimeter=12+35+37=84units for m^or m^2+12;we don't get integer side

Answer 2

Solution :-

We can find length of the other two sides by the formula of Pythagorean Triplets. i.e. 2m, m² - 1 and m² + 1

Let the length of the shortest side of the right angled triangle be 12 units

⇒ 2m = 12

⇒ m = 12/2 

⇒ m = 6 units

Putting the value of m = 6 in m² - 1 and m² + 1

⇒ m² - 1

⇒ 6² - 1

⇒ 36 - 1

⇒ 35

m² + 1

⇒ 6² + 1

⇒ 36 + 1

⇒ 37 Units

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

And,

Perimeter of the triangle = 12 + 35 + 37

84 Units

Answer.