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.

Let’s take the sides of the triangle as 5 * x, 7 * x and 11 * x (ratio 5: 7: 11) and write the equation:
5 * x + 11 * x = 80;
16 * x = 80.
From the resulting expression, we find x:
x = 80/16 = 5.
Thus, we have found the coefficient x. Further, knowing this coefficient, we calculate the length of each side of the triangle:
1) 5 * 5 = 25 (cm);
2) 7 * 5 = 35 (cm);
3) 11 * 5 = 55 (cm).
Find the perimeter (P). The perimeter is the sum of the lengths of all sides of the polygon:
P = 25 + 35 + 55 = 115 (cm),
Answer: the perimeter of the triangle is 115 cm.