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.

Solution: According to 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.