The sides of a triangle are consecutive integers. The perimeter of the triangle is 120 cm. Find the length of the greatest side:

Question: The sides of a triangle are consecutive integers. The perimeter of the triangle is 120 cm. Find the length of the greatest side:

Solution:
Let the sides of the triangles be x cm, (x + 1) cm and (x + 2) cm respectively.
Then,
x + (x + 1) + (x + 2) = 120
⇒ 3x + 3 = 120
⇒ 3x = 117
⇒ x = 39

∴ Length of the greatest side
= (39 + 2) cm
= 41 cm