The perimeter of the triangles is 99 cm. One edge is 9 cm larger than the other, and 2 times larger

The perimeter of the triangles is 99 cm. One edge is 9 cm larger than the other, and 2 times larger than the third. How many cm does each facet have?

To solve this example, we will use the conditional variables “X”, “Y” and “Z”, through which we denote the unknown faces of the triangle.

Using these problems, we will form the following equations:

1) X + Y + Z = 99;

2) X – Y = 9;

3) X / 2 = Z.

Solving a system of three equations with three unknowns, we get X = 2Z.

Substituting X into the second equation, we have 2Z – Y = 9 or Y = 2Z – 9.

Substituting Y and X in the first equation, we have 2Z + 2Z – 9 + Z = 99 or 5Z = 99 + 9 = 108 or Z = 108/5 = 21.6 cm.

Therefore, X = 2 x 21.6 = 43.2 cm, and Y = 2 x 21.6 – 9 = 43.2 – 9 = 34.2 cm.

Answer: the edges of the triangle are 21.6 cm, 34.2 cm and 43.2 cm.