The sides of the triangle are proportional to the numbers 7,8,11. find the largest side if the sum

The sides of the triangle are proportional to the numbers 7,8,11. find the largest side if the sum of the other two sides is 105 cm.

We denote by a one-seventh part of the length of the shorter of the sides of this triangle.

Then the length of this smaller side should be 7a cm.

Since this triangle has a ratio of side lengths of seven to eight to eleven, the lengths of the other two sides should be 8a cm and 11a cm.

Since the sum of the lengths, the length of the smaller sides of this triangle is 105 cm, we can draw up the following equation:

8a + 7a = 105,

solving which, we get:

15a = 105;

a = 105/15 = 7 cm.

We find the length of the larger of the sides:

11a = 11 * 7 = 77 cm.

Answer: 77 cm.