Question

The perimeter of a right angled triangle with integral sides and 5 as the largest side is

___.

Answer 1

Let the other two sides be a and b. According to Pythagoras theorem,

$a^2$ + $b^2$ = $5^2$

$a^2$ + $b^2$ = 25. Since a and b are less than 5, it is easy to note that 25 can be written as the sum of two perfect squares, 16 and 9. So a and b are 4 and 3.

Perimeter of a triangle = sum of the three sides = 3 + 4 + 5 = 12.