Question

in a right angled triangle if the shortest side is 24 cm and the three sides form a Pythagorean triple then what is the length of the largest side?

Answer 1

in right angled triangle ,
the shortest side is 24cm.
Let largest side is a and 3rd side is b.

from Pythagoras theorem,
hypotenuse ² = perpendicular ² + base ²
a² = 24² + b²

A/c to question, three sides form Pythagoras triplet.
Let n be any integer greater than 1, then 3n, 4n and 5n are also a set of Pythagorean Triple. This is true because: (3n)² + (4n)² = (5n)²

here, 3n is smallest side of triangle
so, let 3n = 24 => n = 8
then, 4n = 4 × 8 = 32
and 5n = 5 × 8 = 40

you can check it ,
24² + 32² = 576 + 1024 = 1600 = 40²
hence, (24, 32, 40) is Pythagoras triplet.
so, largest side of triangle is 40cm