The sides of the triangle are 5: 7: 11, and the sum of the largest and smallest sides is 80 cm.

The sides of the triangle are 5: 7: 11, and the sum of the largest and smallest sides is 80 cm. Calculate the perimeter of the triangle.

By the condition of the problem, the sides of the triangle are related as 5: 7: 11. Based on this, we introduce the variable “X”, denoting 1 (one) part. We get 5X: 7X: 11X. Then, the sum of the largest and smallest sides, equal to 80 cm, will be written as 5X + 11X = 80. Hence, 16X = 80 or X = 5. Now we find the lengths of the sides of the triangle, 5 x 5 = 25 cm, 7 x 5 = 35 cm, 11 x 5 = 55 cm. Hence, the perimeter of the triangle will be equal to the sum of the lengths of its sides 25 + 35 + 55 = 115 cm.
Answer: the perimeter of the triangle is 115 cm.