Question

What is the perimeter of a right angled triangle whose smallest side measures 15cm?

Answer 1

If the shortest side is 13 then you can use the two numbers whos squares differ by  132 .

The difference between consecutive squares is consecutive odd numbers.

The difference between  (n)2  and  (n+1)2  is  (2n+1)  

Since our difference is  132=169 , this makes  n  

n=(169–1)/2=84  

So the largest perimeter for a pythagorean triplet using 13 as the shortest side is  (13+84+85)=  182 cm

The shortest perimeter would depend on how many consecutive odd numbers you can sum to 169… and there is only one way, so as the shortest side this is the only pythagorean triplet

Your perimeter is 182 cm

Answer 2

Answer:

If the shortest side is 13 then you can use the two numbers whos squares differ by  132 .

The difference between consecutive squares is consecutive odd numbers.

The difference between  (n)2  and  (n+1)2  is  (2n+1)  

Since our difference is  132=169 , this makes  n  

n=(169–1)/2=84  

So the largest perimeter for a pythagorean triplet using 13 as the shortest side is  (13+84+85)=  182 cm