One side of the triangle is 7 times smaller than the second and 66 cm smaller than the third.

One side of the triangle is 7 times smaller than the second and 66 cm smaller than the third. Find the sides of the triangle if its perimeter is 174 cm.

1) Let x cm be the length of the first side of the triangle.

2) Then 7x cm is the length of the second side, (x + 66) cm is the length of the third side.

3) (x + 7x + (x + 66)) cm – the sum of the lengths of all sides of the triangle, that is, its perimeter.

4) From the condition of the task, you can write:

x + 7x + (x + 66) = 174.

5) Solve the equation and find x:

x + 7x + x + 66 = 174;

9x + 66 = 174;

9x = 174 – 66;

9x = 108;

x = 108: 9;

x = 12.

6) The length of the first side x = 12 cm.

7) Let’s calculate the length of the second side:

12 * 7 = 84 cm.

8) Find out the length of the third party:

12 + 66 = 78 cm.

Answer: 12, 84 and 78 cm.