If the smallest side of a right-angled triangle is 20 cm, then what is the perimeter of the triangle?

It is known that the lengths of sides of a right-angled triangle form a Pythagorean triplet.

The numbers 2m, m² − 1, and m² + 1, where m > 1, form a Pythagorean triplet.

Let 2m = 20

⇒ m = 10

∴ m² − 1 = 10² − 1 = 100 − 1 = 99

m² + 1 = 10² + 1 = 100 + 1 = 101

Therefore, the lengths of other two sides of the triangle are 99 cm and 101 cm.

∴ Perimeter of ΔABC = 20 cm + 99 cm + 101 cm

                               = 220 cm

Thus, the perimeter of the triangle is 220 cm.